(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 9.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       157,          7]
NotebookDataLength[    313072,       7055]
NotebookOptionsPosition[    305532,       6828]
NotebookOutlinePosition[    306122,       6849]
CellTagsIndexPosition[    306079,       6846]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[TextData[{
 "\n",
 StyleBox["Line\[AAcute]ris h\[AAcute]rom v\[AAcute]ltoz\[OAcute]s homog\
\[EAcute]n \[EAcute]s inhomog\[EAcute]n egyenletrendszerek grafikus bemutat\
\[AAcute]sa.\n\nK\[EAcute]sz\[IAcute]tette: Wiandt Zs\[OAcute]fia \[EAcute]s \
Torma G\[AAcute]bor",
  FontSize->36],
 "\n"
}], "Section",
 CellChangeTimes->{{3.6651487832819157`*^9, 3.6651488072209225`*^9}, {
   3.665148839331395*^9, 3.6651488730869675`*^9}, 3.665152126557625*^9, {
   3.6658235841747465`*^9, 3.665823586860539*^9}, {3.666690573012744*^9, 
   3.6666906075938053`*^9}, {3.666690734344296*^9, 3.666690767190194*^9}},
 TextAlignment->Center,
 FontColor->RGBColor[
  0.7607843137254902, 0.29411764705882354`, 0.08235294117647059]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Elm\[EAcute]leti h\[AAcute]tt\[EAcute]r",
 FontFamily->"Arial",
 FontWeight->"Bold",
 FontSlant->"Italic"]], "Section",
 CellChangeTimes->{{3.6651490345279274`*^9, 3.6651490435789795`*^9}, {
  3.6665234544738507`*^9, 3.6665234553619013`*^9}},
 TextJustification->1.],

Cell[TextData[{
 "Az\n\n\t",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "1"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   RowBox[{
    SubscriptBox["a", "2"], "\[CenterDot]", 
    SubscriptBox["x", "2"]}], TraditionalForm]]],
 "+...+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "n"], TraditionalForm]]],
 Cell[BoxData[
  FormBox[
   RowBox[{"\[CenterDot]", 
    SubscriptBox["x", "n"]}], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox["b", TraditionalForm]]],
 "\n\nalakra hozhat\[OAcute] egyenletet ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 ", ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 ", ... , ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "n"], TraditionalForm]]],
 " ismeretlenekben line\[AAcute]ris egyenletnek nevezz\[UDoubleDot]k, ahol ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "1"], TraditionalForm]]],
 ", ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "2"], TraditionalForm]]],
 ", ... , ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "n"], TraditionalForm]]],
 ", valamint ",
 Cell[BoxData[
  FormBox["b", TraditionalForm]]],
 " konstansok. Az ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    SubscriptBox["a", "1"], ",", " ", 
    SubscriptBox["a", "2"], ",", " ", "...", " ", ",", " ", 
    RowBox[{
     SubscriptBox["a", "n"], " ", "konstansokat", " ", "az", " ", "egyenlet", 
     " ", "egy\[UDoubleDot]tthat\[OAcute]inak"}], ",", " ", "b", " "}], 
   TraditionalForm]]],
 "-t az egyenlet konstans tagj\[AAcute]nak nevezz\[UDoubleDot]k."
}], "Text",
 CellChangeTimes->{{3.666524516157785*^9, 3.666524600927693*^9}, {
  3.666524721410355*^9, 3.66652479334947*^9}, {3.666524935524602*^9, 
  3.6665249413049326`*^9}, {3.6665251570472727`*^9, 3.666525158809373*^9}, {
  3.666529946740227*^9, 3.6665299495093856`*^9}, {3.666530015041134*^9, 
  3.666530230477456*^9}},
 TextJustification->1.],

Cell["\<\
Line\[AAcute]ris egyenletek egy halmaz\[AAcute]t line\[AAcute]ris \
egyenletrendszernek nevezz\[UDoubleDot]k. Az egyenletrendszer ismeretlenei \
mindazok az ismeretlenek, amelyek legal\[AAcute]bb egy egyenletben \
szerepelnek. Ha egy ismeretlen egy egyenletben szerepel, de egy \
m\[AAcute]sikban nem, akkor ez ut\[OAcute]bbiban \[UAcute]gy tekintj\
\[UDoubleDot]k, hogy az adott ismeretlennek 0 az egy\[UDoubleDot]tthat\
\[OAcute]ja.\
\>", "Text",
 CellChangeTimes->{{3.666530696883133*^9, 3.66653072655683*^9}, {
  3.6665308007720747`*^9, 3.666530861507549*^9}},
 TextJustification->1.],

Cell[TextData[{
 "A line\[AAcute]ris egyenletrendszer teh\[AAcute]t olyan \
t\[ODoubleDot]bbismeretlenes egyenletrendszer, ahol minden ismeretlen els\
\[ODoubleAcute] hatv\[AAcute]nyon szerepel.\n\nN\[EAcute]zz\[UDoubleDot]k \
most csak a 3 v\[AAcute]ltoz\[OAcute]s line\[AAcute]ris egyenletrendszereket. \
Ez azon line\[AAcute]ris egyenletek egy halmaz\[AAcute]t jelenti, ahol minden \
egyenletben ugyanaz a 3 ismeretlen szerepel, teh\[AAcute]t a bel\
\[ODoubleAcute]l\[UDoubleDot]k alkotott line\[AAcute]ris egyenletrendszerben \
\[ODoubleDot]sszesen 3 ismeretlen szerepel.\n\nEgy m \
egyenletb\[ODoubleAcute]l \[AAcute]ll\[OAcute] \[EAcute]s 3 ismeretlent \
tartalmaz\[OAcute] line\[AAcute]ris egyenletrendszer:\n\n\t",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "11"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "12"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "13"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   SubscriptBox["b", "1"], TraditionalForm]]],
 "\n\t",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "21"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "22"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "23"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   SubscriptBox["b", "2"], TraditionalForm]]],
 "\n\t",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "31"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "32"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "33"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   SubscriptBox["b", "3"], TraditionalForm]]],
 "\n\t\[VerticalEllipsis]\n\t",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "m1"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "m2"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "m3"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   SubscriptBox["b", "m"], TraditionalForm]]],
 "\n\nAmennyiben \[ForAll]",
 StyleBox[" i",
  FontSlant->"Italic"],
 " \[Element] (1, m) eset\[EAcute]n ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["b", "i"], TraditionalForm]],
  FontSlant->"Italic"],
 StyleBox["=0, ",
  FontSlant->"Italic"],
 "akkor homog\[EAcute]n egyenletrendszerr\[ODoubleAcute]l besz\[EAcute]l\
\[UDoubleDot]nk. Minden m\[AAcute]s esetben, azaz ha \[Exists] i \[Element] \
(1, m), hogy ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["b", "i"], TraditionalForm]],
  FontSlant->"Italic"],
 "\[NotEqual]0, akkor inhomog\[EAcute]n egyenletrendszerr\[ODoubleAcute]l \
besz\[EAcute]l\[UDoubleDot]nk.\n\nAz egyenletrendszer vektori\[AAcute]lis \
alakja:\n\n\t",
 Cell[BoxData[
  FormBox[
   RowBox[{"(", GridBox[{
      {
       SubscriptBox["a", "11"]},
      {
       SubscriptBox["a", "21"]},
      {
       SubscriptBox["a", "31"]},
      {"\[VerticalEllipsis]"},
      {
       SubscriptBox["a", "m1"]}
     }], ")"}], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   RowBox[{"(", GridBox[{
      {
       SubscriptBox["a", "12"]},
      {
       SubscriptBox["a", "22"]},
      {
       SubscriptBox["a", "32"]},
      {"\[VerticalEllipsis]"},
      {
       SubscriptBox["a", "m2"]}
     }], ")"}], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   RowBox[{"(", GridBox[{
      {
       SubscriptBox["a", "13"]},
      {
       SubscriptBox["a", "23"]},
      {
       SubscriptBox["a", "33"]},
      {"\[VerticalEllipsis]"},
      {
       SubscriptBox["a", "m3"]}
     }], ")"}], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   RowBox[{"(", GridBox[{
      {
       SubscriptBox["b", "1"]},
      {
       SubscriptBox["b", "2"]},
      {
       SubscriptBox["b", "3"]},
      {"\[VerticalEllipsis]"},
      {
       SubscriptBox["b", "m"]}
     }], ")"}], TraditionalForm]]],
 "\n\t\nEkkor a line\[AAcute]ris egyenletrendszer egy\[UDoubleDot]tthat\
\[OAcute]ib\[OAcute]l \[AAcute]ll\[OAcute] oszlopvektorok olyan \
line\[AAcute]ris kombin\[AAcute]ci\[OAcute]j\[AAcute]t keress\[UDoubleDot]k, \
amely a ",
 Cell[BoxData[
  FormBox[
   RowBox[{"(", GridBox[{
      {
       SubscriptBox["b", "1"]},
      {
       SubscriptBox["b", "2"]},
      {
       SubscriptBox["b", "3"]},
      {"\[VerticalEllipsis]"},
      {
       SubscriptBox["b", "m"]}
     }], ")"}], TraditionalForm]]],
 " vektorral megegyezik.\n\[CapitalIAcute]gy a feladat m\[AAcute]r grafikusan \
is szeml\[EAcute]ltethet\[ODoubleAcute]."
}], "Text",
 CellChangeTimes->{{3.665149059841857*^9, 3.6651491665392056`*^9}, {
   3.665149237698795*^9, 3.665149403959976*^9}, {3.6651494357262163`*^9, 
   3.6651495590326757`*^9}, {3.6651496018142815`*^9, 
   3.6651496378333683`*^9}, {3.665149683644002*^9, 3.665149740224844*^9}, {
   3.6651497714457197`*^9, 3.6651497895087957`*^9}, {3.6651498730946927`*^9, 
   3.6651499132835712`*^9}, {3.665150138700306*^9, 3.6651502130440216`*^9}, {
   3.6651502578800035`*^9, 3.665150289892414*^9}, {3.6651508531981044`*^9, 
   3.66515112753456*^9}, {3.665152141861858*^9, 3.665152143529974*^9}, {
   3.665327037852871*^9, 3.665327037852871*^9}, 3.6658236266840897`*^9, {
   3.66582366009536*^9, 3.665824174839522*^9}, {3.665824214262806*^9, 
   3.6658242976654067`*^9}, {3.666523893606968*^9, 3.6665238962551193`*^9}, {
   3.666530896127529*^9, 3.6665308969405756`*^9}, {3.666530941992152*^9, 
   3.6665309905799313`*^9}, {3.66653104650613*^9, 3.6665314348503423`*^9}, {
   3.6665315086325626`*^9, 3.6665315864680142`*^9}, {3.6665317292561812`*^9, 
   3.666531732490366*^9}, {3.666532743833212*^9, 3.6665328391129484`*^9}, {
   3.666535847805873*^9, 3.6665358534091935`*^9}, {3.666536365196466*^9, 
   3.6665364442679887`*^9}, {3.666536776738595*^9, 3.6665368002976313`*^9}, {
   3.666537025989956*^9, 3.666537040234976*^9}},
 TextJustification->1.]
}, Open  ]],

Cell[CellGroupData[{

Cell["Grafikus \[AAcute]br\[AAcute]zol\[AAcute]s I.", "Section",
 CellChangeTimes->{{3.6665370126199374`*^9, 3.666537018639946*^9}, {
  3.667220738263353*^9, 3.6672207407634954`*^9}},
 TextJustification->1.,
 FontWeight->"Bold",
 FontSlant->"Italic"],

Cell[CellGroupData[{

Cell["Inhomog\[EAcute]n line\[AAcute]ris egyenletrendszerek", "Subsection",
 CellChangeTimes->{{3.6665387981575356`*^9, 3.666538799377537*^9}, {
  3.6665388555276155`*^9, 3.6665388693626347`*^9}, {3.6665391413860245`*^9, 
  3.6665391422710257`*^9}},
 TextJustification->1.,
 FontWeight->"Bold",
 FontSlant->"Italic"],

Cell["\<\
Els\[ODoubleAcute] esetben vegy\[UDoubleDot]k az inhomog\[EAcute]n \
egyenletrendszereket.

N\[EAcute]zz\[UDoubleDot]k el\[ODoubleAcute]sz\[ODoubleDot]r meg k\[EAcute]t \
dimenzi\[OAcute]ban, hogy mit is kell majd csin\[AAcute]lni h\[AAcute]rom \
dimenzi\[OAcute]ban.
\
\>", "Text",
 CellChangeTimes->{{3.666537031119963*^9, 3.6665370440599813`*^9}, {
  3.6665373258533897`*^9, 3.666537373198456*^9}},
 TextJustification->1.],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"Graphics", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"Red", ",", 
       RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
       RowBox[{"Arrow", "[", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"0", ",", "0"}], "}"}], ",", 
          RowBox[{"{", 
           RowBox[{"1", ",", "3"}], "}"}]}], "}"}], "]"}]}], "}"}], ",", 
     RowBox[{"Axes", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"True", ",", "True"}], "}"}]}], ",", 
     RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
     RowBox[{"AxesOrigin", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0"}], "}"}]}]}], "]"}], ",", 
   RowBox[{"Graphics", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"Green", ",", 
       RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
       RowBox[{"Arrow", "[", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"1", ",", "3"}], "}"}], ",", 
          RowBox[{"{", 
           RowBox[{"6", ",", "4"}], "}"}]}], "}"}], "]"}]}], "}"}], ",", 
     RowBox[{"Axes", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"True", ",", "True"}], "}"}]}], ",", 
     RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
     RowBox[{"AxesOrigin", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0"}], "}"}]}]}], "]"}], ",", 
   RowBox[{"Graphics", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"Blue", ",", 
       RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
       RowBox[{"Arrow", "[", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"6", ",", "4"}], "}"}], ",", 
          RowBox[{"{", 
           RowBox[{"10", ",", "4"}], "}"}]}], "}"}], "]"}]}], "}"}], ",", 
     RowBox[{"Axes", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"True", ",", "True"}], "}"}]}], ",", 
     RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
     RowBox[{"AxesOrigin", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0"}], "}"}]}]}], "]"}], ",", 
   RowBox[{"Graphics", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"Purple", ",", 
       RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
       RowBox[{"Arrow", "[", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"0", ",", "0"}], "}"}], ",", 
          RowBox[{"{", 
           RowBox[{"10", ",", "4"}], "}"}]}], "}"}], "]"}]}], "}"}], ",", 
     RowBox[{"Axes", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"True", ",", "True"}], "}"}]}], ",", 
     RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
     RowBox[{"AxesOrigin", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0"}], "}"}]}]}], "]"}]}], "]"}]], "Input",
 TextJustification->1.],

Cell[BoxData[
 GraphicsBox[{
   {RGBColor[1, 0, 0], PointSize[0.1], ArrowBox[{{0, 0}, {1, 3}}]}, 
   {RGBColor[0, 1, 0], PointSize[0.1], ArrowBox[{{1, 3}, {6, 4}}]}, 
   {RGBColor[0, 0, 1], PointSize[0.1], ArrowBox[{{6, 4}, {10, 4}}]}, 
   {RGBColor[0.5, 0, 0.5], PointSize[0.1], ArrowBox[{{0, 0}, {10, 4}}]}},
  AspectRatio->1,
  Axes->{True, True},
  AxesOrigin->{0, 0}]], "Output",
 CellChangeTimes->{3.6665367901576166`*^9},
 TextJustification->1.]
}, {2}]],

Cell[TextData[{
 "Legyen a piros vektor mindig az ",
 Cell[BoxData[
  FormBox[
   RowBox[{"(", GridBox[{
      {
       SubscriptBox["a", "11"]},
      {
       SubscriptBox["a", "21"]},
      {
       SubscriptBox["a", "31"]},
      {"\[VerticalEllipsis]"},
      {
       SubscriptBox["a", "m1"]}
     }], ")"}], TraditionalForm]]],
 " vektor sz\[AAcute]mszorosa (",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "-szerese), ez induljon mindig az orig\[OAcute]b\[OAcute]l. A piros vektor v\
\[EAcute]gpontj\[AAcute]b\[OAcute]l induljon a z\[ODoubleDot]ld vektor, ami \
az ",
 Cell[BoxData[
  FormBox[
   RowBox[{"(", GridBox[{
      {
       SubscriptBox["a", "12"]},
      {
       SubscriptBox["a", "22"]},
      {
       SubscriptBox["a", "32"]},
      {"\[VerticalEllipsis]"},
      {
       SubscriptBox["a", "m2"]}
     }], ")"}], TraditionalForm]]],
 " vektor sz\[AAcute]mszorosa (",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "-szerese), majd ennek a v\[EAcute]gpontj\[AAcute]b\[OAcute]l induljon a k\
\[EAcute]k vektor, az ",
 Cell[BoxData[
  FormBox[
   RowBox[{"(", GridBox[{
      {
       SubscriptBox["a", "13"]},
      {
       SubscriptBox["a", "23"]},
      {
       SubscriptBox["a", "33"]},
      {"\[VerticalEllipsis]"},
      {
       SubscriptBox["a", "m3"]}
     }], ")"}], TraditionalForm]]],
 " vektor sz\[AAcute]mszorosa (",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "-szorosa). \[CapitalEAcute]s \[IAcute]gy a k\[EAcute]k vektor \
v\[EAcute]gpontja a lila vektor, azaz a ",
 Cell[BoxData[
  FormBox[
   RowBox[{"(", GridBox[{
      {
       SubscriptBox["b", "1"]},
      {
       SubscriptBox["b", "2"]},
      {
       SubscriptBox["b", "3"]},
      {"\[VerticalEllipsis]"},
      {
       SubscriptBox["b", "m"]}
     }], ")"}], TraditionalForm]]],
 " vektor v\[EAcute]gpontj\[AAcute]ba kell mutasson. Ha ez \
teljes\[UDoubleDot]l, akkor az (",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 ",",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 ", ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 ") sz\[AAcute]mh\[AAcute]rmas megold\[AAcute]sa az egyenletrendszernek. \
(Azzal, hogy egy vektort megszorzunk egy sz\[AAcute]mmal, az ir\[AAcute]nya \
nem fog v\[AAcute]ltozni, csak a vektor hossza.)"
}], "Text",
 CellChangeTimes->{{3.666537061015005*^9, 3.666537306793363*^9}, {
  3.666537391158481*^9, 3.6665374397485495`*^9}, {3.66654329942959*^9, 
  3.6665433001310625`*^9}, {3.6665449636046724`*^9, 3.666545005071044*^9}},
 TextJustification->1.],

Cell["\<\



N\[EAcute]zz\[UDoubleDot]k most akkor ezek ut\[AAcute]n h\[AAcute]rom dimenzi\
\[OAcute]ban az eg\[EAcute]szet. Legyen adva egy 3 egyenletb\[ODoubleAcute]l \
\[EAcute]s 3 ismeretlenb\[ODoubleAcute]l \[AAcute]ll\[OAcute] \
line\[AAcute]ris egyenletrendszer:\
\>", "Text",
 CellChangeTimes->{{3.6665375567717514`*^9, 3.6665376146938334`*^9}, {
  3.666543304008646*^9, 3.6665433070887218`*^9}},
 TextJustification->1.],

Cell[TextData[{
 "\t1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+5\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+4\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=4\n\t3\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+0\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0\n\t1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+9\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+6\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=1\n\t\nItt a piros vektor a k\[ODoubleDot]vetkez\[ODoubleAcute] lesz:  ",
 Cell[BoxData[
  FormBox[
   RowBox[{"(", GridBox[{
      {"1"},
      {"3"},
      {"1"}
     }], ")"}], TraditionalForm]]],
 ".\nA z\[ODoubleDot]ld vektor ez lesz:  ",
 Cell[BoxData[
  FormBox[
   RowBox[{"(", GridBox[{
      {"5"},
      {"1"},
      {"9"}
     }], ")"}], TraditionalForm]]],
 ".\nA k\[EAcute]k vektor ez lesz:  ",
 Cell[BoxData[
  FormBox[
   RowBox[{"(", GridBox[{
      {"4"},
      {"0"},
      {"6"}
     }], ")"}], TraditionalForm]]],
 ".\nA lila vektor pedig ez lesz:  ",
 Cell[BoxData[
  FormBox[
   RowBox[{"(", GridBox[{
      {"4"},
      {"0"},
      {"1"}
     }], ")"}], TraditionalForm]]],
 ".\nHa ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=1 esetet n\[EAcute]zz\[UDoubleDot]k, azaz amikor a vektorokat \
\[OpenCurlyDoubleQuote]\[ODoubleDot]nmagukban\[CloseCurlyDoubleQuote] \
\[AAcute]br\[AAcute]zoljuk, vagyis amikor m\[EAcute]g nincsenek megszorozva \
semmilyen (1-t\[ODoubleAcute]l k\[UDoubleDot]l\[ODoubleDot]nb\[ODoubleDot]z\
\[ODoubleAcute]) sz\[AAcute]mmal, akkor a \
k\[ODoubleDot]vetkez\[ODoubleAcute]k\[EAcute]ppen n\[EAcute]z ki \
h\[AAcute]rom dimenzi\[OAcute]ban az, amit az el\[ODoubleAcute]bb k\[EAcute]t \
dimenzi\[OAcute]ban l\[AAcute]ttunk:\n\n"
}], "Text",
 CellChangeTimes->{{3.6665379740463386`*^9, 3.6665383326298456`*^9}, {
  3.666546805083502*^9, 3.6665468121682243`*^9}, {3.666546886806984*^9, 
  3.6665468925838366`*^9}, {3.6665469554207225`*^9, 3.666547002263956*^9}},
 TextJustification->1.],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"Graphics3D", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"Red", ",", 
       RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
       RowBox[{"Arrow", "[", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", 
          RowBox[{"{", 
           RowBox[{"1", ",", "3", ",", "1"}], "}"}]}], "}"}], "]"}]}], "}"}], 
     ",", 
     RowBox[{"Axes", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], ",", 
     RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
     RowBox[{"AxesOrigin", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
   RowBox[{"Graphics3D", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"Green", ",", 
       RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
       RowBox[{"Arrow", "[", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"1", ",", "3", ",", "1"}], "}"}], ",", 
          RowBox[{"{", 
           RowBox[{"6", ",", "4", ",", "10"}], "}"}]}], "}"}], "]"}]}], "}"}],
      ",", 
     RowBox[{"Axes", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], ",", 
     RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
     RowBox[{"AxesOrigin", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
   RowBox[{"Graphics3D", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"Blue", ",", 
       RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
       RowBox[{"Arrow", "[", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"6", ",", "4", ",", "10"}], "}"}], ",", 
          RowBox[{"{", 
           RowBox[{"10", ",", "4", ",", "16"}], "}"}]}], "}"}], "]"}]}], 
      "}"}], ",", 
     RowBox[{"Axes", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], ",", 
     RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
     RowBox[{"AxesOrigin", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
   RowBox[{"Graphics3D", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"Purple", ",", 
       RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
       RowBox[{"Arrow", "[", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", 
          RowBox[{"{", 
           RowBox[{"4", ",", "0", ",", "1"}], "}"}]}], "}"}], "]"}]}], "}"}], 
     ",", 
     RowBox[{"Axes", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], ",", 
     RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
     RowBox[{"AxesOrigin", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}]}], "]"}]], "Input",
 TextJustification->1.],

Cell[BoxData[
 Graphics3DBox[{
   {RGBColor[1, 0, 0], PointSize[0.1], Arrow3DBox[{{0, 0, 0}, {1, 3, 1}}]}, 
   {RGBColor[0, 1, 0], PointSize[0.1], Arrow3DBox[{{1, 3, 1}, {6, 4, 10}}]}, 
   {RGBColor[0, 0, 1], PointSize[0.1], Arrow3DBox[{{6, 4, 10}, {10, 4, 16}}]}, 
   {RGBColor[0.5, 0, 0.5], PointSize[0.1], 
    Arrow3DBox[{{0, 0, 0}, {4, 0, 1}}]}},
  AspectRatio->1,
  Axes->{True, True, True},
  AxesOrigin->{0, 0, 0}]], "Output",
 CellChangeTimes->{3.6665375368847213`*^9},
 TextJustification->1.,ImageCache->GraphicsData["CompressedBitmap", "\<\
[encoded data, 9300 characters]
tZC9CfmSZ8pMShoxZhY2lh52C/TfxKTVtP8HhRgebA==\
\>"]]
}, {2}]],

Cell[TextData[{
 "L\[AAcute]szik, hogy nem a lila vektor v\[EAcute]gpontj\[AAcute]ban van a k\
\[EAcute]k vektor v\[EAcute]gpontja, azaz keresn\[UDoubleDot]nk kell 3 \
megfelel\[ODoubleAcute] sz\[AAcute]mot ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 ", ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 " \[EAcute]s ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 " hely\[EAcute]re, amivel megszorozva a megfelel\[ODoubleAcute] vektorokat, \
\[EAcute]ppen a lila vektor v\[EAcute]gpontj\[AAcute]ba fog mutatni a k\
\[EAcute]k vektor.\n\nN\[EAcute]zz\[UDoubleDot]k is ezt. \
Pr\[OAcute]b\[AAcute]ljunk meg megfelel\[ODoubleAcute] ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "-t, ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "-t, \[EAcute]s ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "-t keresni.\n"
}], "Text",
 CellChangeTimes->{{3.6665383403348565`*^9, 3.6665384119549565`*^9}, {
  3.6665384428630047`*^9, 3.6665384875130672`*^9}, {3.6665450313045444`*^9, 
  3.6665450614052663`*^9}},
 TextJustification->1.],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Manipulate", "[", 
  RowBox[{
   RowBox[{"Show", "[", 
    RowBox[{
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Purple", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", 
            RowBox[{"{", 
             RowBox[{"4", ",", "0", ",", "1"}], "}"}]}], "}"}], "]"}]}], 
        "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Red", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{"1", "*", "x1"}], ",", 
              RowBox[{"3", "*", "x1"}], ",", 
              RowBox[{"1", "*", "x1"}]}], "}"}]}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Green", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{
              RowBox[{"1", "*", "x1"}], ",", 
              RowBox[{"3", "*", "x1"}], ",", 
              RowBox[{"1", "*", "x1"}]}], "}"}], ",", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{
               RowBox[{"1", "*", "x1"}], "+", 
               RowBox[{"5", "*", "x2"}]}], ",", 
              RowBox[{
               RowBox[{"3", "*", "x1"}], "+", 
               RowBox[{"1", "*", "x2"}]}], ",", 
              RowBox[{
               RowBox[{"1", "*", "x1"}], "+", 
               RowBox[{"9", "*", "x2"}]}]}], "}"}]}], "}"}], "]"}]}], "}"}], 
       ",", 
       RowBox[{"Axes", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Blue", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{
              RowBox[{
               RowBox[{"1", "*", "x1"}], "+", 
               RowBox[{"5", "*", "x2"}]}], ",", 
              RowBox[{
               RowBox[{"3", "*", "x1"}], "+", 
               RowBox[{"1", "*", "x2"}]}], ",", 
              RowBox[{
               RowBox[{"1", "*", "x1"}], "+", 
               RowBox[{"9", "*", "x2"}]}]}], "}"}], ",", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{
               RowBox[{"1", "*", "x1"}], "+", 
               RowBox[{"5", "*", "x2"}], "+", 
               RowBox[{"4", "*", "x3"}]}], ",", 
              RowBox[{
               RowBox[{"3", "*", "x1"}], "+", 
               RowBox[{"1", "*", "x2"}], "+", 
               RowBox[{"0", "*", "x3"}]}], ",", 
              RowBox[{
               RowBox[{"1", "*", "x1"}], "+", 
               RowBox[{"9", "*", "x2"}], "+", 
               RowBox[{"6", "*", "x3"}]}]}], "}"}]}], "}"}], "]"}]}], "}"}], 
       ",", 
       RowBox[{"Axes", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x1", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x2", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x3", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"SaveDefinitions", "\[Rule]", "True"}]}], "]"}]], "Input",
 TextJustification->1.],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`x1$$ = -100., $CellContext`x2$$ = -100., \
$CellContext`x3$$ = -100, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, 
    Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 
    1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{
      Hold[$CellContext`x1$$], -100, 100}, {
      Hold[$CellContext`x2$$], -100, 100}, {
      Hold[$CellContext`x3$$], -100, 100}}, Typeset`size$$ = {
    360., {177., 182.}}, Typeset`update$$ = 0, Typeset`initDone$$, 
    Typeset`skipInitDone$$ = True, $CellContext`x1$1927$$ = 
    0, $CellContext`x2$1928$$ = 0, $CellContext`x3$1929$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`x1$$ = -100, $CellContext`x2$$ = -100, \
$CellContext`x3$$ = -100}, "ControllerVariables" :> {
        Hold[$CellContext`x1$$, $CellContext`x1$1927$$, 0], 
        Hold[$CellContext`x2$$, $CellContext`x2$1928$$, 0], 
        Hold[$CellContext`x3$$, $CellContext`x3$1929$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, "Body" :> Show[
        Graphics3D[{Purple, 
          PointSize[0.1], 
          Arrow[{{0, 0, 0}, {4, 0, 1}}]}, Axes -> {True, True, True}, 
         AspectRatio -> 1, AxesOrigin -> {0, 0, 0}], 
        Graphics3D[{Red, 
          PointSize[0.1], 
          
          Arrow[{{0, 0, 0}, {
            1 $CellContext`x1$$, 3 $CellContext`x1$$, 1 $CellContext`x1$$}}]},
          Axes -> {True, True, True}, AspectRatio -> 1, 
         AxesOrigin -> {0, 0, 0}], 
        Graphics3D[{Green, 
          PointSize[0.1], 
          
          Arrow[{{1 $CellContext`x1$$, 3 $CellContext`x1$$, 
             1 $CellContext`x1$$}, {
            1 $CellContext`x1$$ + 5 $CellContext`x2$$, 3 $CellContext`x1$$ + 
             1 $CellContext`x2$$, 1 $CellContext`x1$$ + 
             9 $CellContext`x2$$}}]}, Axes -> {True, True, True}, AspectRatio -> 
         1, AxesOrigin -> {0, 0, 0}], 
        Graphics3D[{Blue, 
          PointSize[0.1], 
          
          Arrow[{{1 $CellContext`x1$$ + 5 $CellContext`x2$$, 
             3 $CellContext`x1$$ + 1 $CellContext`x2$$, 1 $CellContext`x1$$ + 
             9 $CellContext`x2$$}, {
            1 $CellContext`x1$$ + 5 $CellContext`x2$$ + 4 $CellContext`x3$$, 
             3 $CellContext`x1$$ + 1 $CellContext`x2$$ + 0 $CellContext`x3$$, 
             1 $CellContext`x1$$ + 9 $CellContext`x2$$ + 
             6 $CellContext`x3$$}}]}, Axes -> {True, True, True}, AspectRatio -> 
         1, AxesOrigin -> {0, 0, 0}]], 
      "Specifications" :> {{$CellContext`x1$$, -100, 
         100}, {$CellContext`x2$$, -100, 100}, {$CellContext`x3$$, -100, 
         100}}, "Options" :> {}, "DefaultOptions" :> {}],
     ImageSizeCache->{411., {251., 256.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    SynchronousInitialization->True,
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{3.6665384225669727`*^9, 3.666543435415249*^9},
 TextJustification->1.]
}, {2}]],

Cell["\<\

Nem sok\[AAcute]ra l\[AAcute]tni fogjuk, hogy mik is a j\[OAcute] \
v\[AAcute]laszt\[AAcute]sok. De el\[ODoubleAcute]sz\[ODoubleDot]r haladjunk \
egy kicsit tov\[AAcute]bb.

N\[EAcute]zz\[UDoubleDot]k meg a v\[AAcute]ltoz\[OAcute]k sz\[AAcute]ma, \
\[EAcute]s a f\[UDoubleDot]ggetlen egyenletek sz\[AAcute]ma k\[ODoubleDot]z\
\[ODoubleDot]tti kapcsolatot.\
\>", "Text",
 CellChangeTimes->{{3.666538627305289*^9, 3.6665387047723985`*^9}},
 TextJustification->1.]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
A v\[AAcute]ltoz\[OAcute]k sz\[AAcute]ma, \[EAcute]s a f\[UDoubleDot]ggetlen \
egyenletek sz\[AAcute]ma k\[ODoubleDot]z\[ODoubleDot]tti kapcsolat\
\>", "Subsection",
 CellChangeTimes->{{3.6665387401454525`*^9, 3.6665387579054775`*^9}, {
  3.6665393558804383`*^9, 3.6665393689554567`*^9}},
 TextJustification->1.,
 FontWeight->"Bold",
 FontSlant->"Italic"],

Cell["\<\
F\[UDoubleDot]ggetlen egyenletek: h\[AAcute]rom egyenlet \
f\[UDoubleDot]ggetlen, ha egyik egyenlet sem sz\[AAcute]mszorosa egy m\
\[AAcute]siknak, illetve egyik egyenlet sem \[AAcute]ll el\[ODoubleAcute] a m\
\[AAcute]sik k\[EAcute]t egyenlet line\[AAcute]ris \
kombin\[AAcute]ci\[OAcute]jak\[EAcute]nt.\
\>", "Text",
 CellChangeTimes->{{3.6665393753604655`*^9, 3.666539430697544*^9}},
 TextJustification->1.],

Cell[CellGroupData[{

Cell["\<\
1. eset: A f\[UDoubleDot]ggetlen egyenletek sz\[AAcute]ma \[EAcute]s a v\
\[AAcute]ltoz\[OAcute]k sz\[AAcute]ma egyenl\[ODoubleAcute]: 3 \
f\[UDoubleDot]ggetlen egyenlet, 3 v\[AAcute]ltoz\[OAcute]\
\>", "Subsubsection",
 CellChangeTimes->{{3.6665392604483037`*^9, 3.6665393408154173`*^9}, 
   3.6665394350925503`*^9, {3.666540528145979*^9, 3.6665405604438257`*^9}, 
   3.6665483854971094`*^9},
 TextJustification->1.,
 FontWeight->"Bold",
 FontSlant->"Italic"],

Cell["\<\
N\[EAcute]zz\[UDoubleDot]k meg az el\[ODoubleAcute]z\[ODoubleAcute] \
egyenletrendszert, arra igaz lesz, hogy h\[AAcute]rom \
v\[AAcute]ltoz\[OAcute]t tartalmaz, \[EAcute]s az egyenletek \
f\[UDoubleDot]ggetlenek.\
\>", "Text",
 CellChangeTimes->{{3.666540089391883*^9, 3.66654016119599*^9}},
 TextJustification->1.],

Cell[TextData[{
 "\t1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+5\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+4\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=4\n\t3\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+0\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0\n\t1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+9\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+6\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=1"
}], "Text",
 CellChangeTimes->{{3.6665401939428635`*^9, 3.666540197068042*^9}, {
  3.6665470438026447`*^9, 3.666547063954081*^9}},
 TextJustification->1.],

Cell["\<\
N\[EAcute]zz\[UDoubleDot]k ugyanazt az \[AAcute]br\[AAcute]t, mint az el\
\[ODoubleAcute]bb. A feladat ugyanaz. A k\[EAcute]k vektor v\[EAcute]gpontja \
a lila vektor v\[EAcute]gpontj\[AAcute]ban kell legyen.\
\>", "Text",
 CellChangeTimes->{{3.666540219723338*^9, 3.6665402634038363`*^9}},
 TextJustification->1.],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"o", "=", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"v11", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "3", ",", "1"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"v12", "=", 
   RowBox[{"{", 
    RowBox[{"5", ",", "1", ",", "9"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"v13", "=", 
   RowBox[{"{", 
    RowBox[{"4", ",", "0", ",", "6"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"v14", "=", 
   RowBox[{"{", 
    RowBox[{"4", ",", "0", ",", "1"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"Manipulate", "[", 
  RowBox[{
   RowBox[{"Show", "[", 
    RowBox[{
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Purple", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{"o", ",", "v14"}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Red", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{"o", ",", 
            RowBox[{"x1", "*", "v11"}]}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Green", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"x1", "*", "v11"}], ",", 
            RowBox[{
             RowBox[{"x1", "*", "v11"}], "+", 
             RowBox[{"x2", "*", "v12"}]}]}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Blue", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{
             RowBox[{"x1", "*", "v11"}], "+", 
             RowBox[{"x2", "*", "v12"}]}], ",", 
            RowBox[{
             RowBox[{"x1", "*", "v11"}], "+", 
             RowBox[{"x2", "*", "v12"}], "+", 
             RowBox[{"x3", "*", "v13"}]}]}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x1", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x2", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x3", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"SaveDefinitions", "\[Rule]", "True"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.66653970881409*^9, 3.666539730246122*^9}, {
  3.6665398001882296`*^9, 3.666539805513237*^9}},
 TextJustification->1.],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`x1$$ = -100, $CellContext`x2$$ = -100., \
$CellContext`x3$$ = -100., Typeset`show$$ = True, Typeset`bookmarkList$$ = {},
     Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 
    1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{
      Hold[$CellContext`x1$$], -100, 100}, {
      Hold[$CellContext`x2$$], -100, 100}, {
      Hold[$CellContext`x3$$], -100, 100}}, Typeset`size$$ = {
    360., {177., 182.}}, Typeset`update$$ = 0, Typeset`initDone$$, 
    Typeset`skipInitDone$$ = False, $CellContext`x1$2549$$ = 
    0, $CellContext`x2$2550$$ = 0, $CellContext`x3$2551$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`x1$$ = -100, $CellContext`x2$$ = -100, \
$CellContext`x3$$ = -100}, "ControllerVariables" :> {
        Hold[$CellContext`x1$$, $CellContext`x1$2549$$, 0], 
        Hold[$CellContext`x2$$, $CellContext`x2$2550$$, 0], 
        Hold[$CellContext`x3$$, $CellContext`x3$2551$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, "Body" :> Show[
        Graphics3D[{Purple, 
          PointSize[0.1], 
          Arrow[{$CellContext`o, $CellContext`v14}]}, Axes -> True, 
         AspectRatio -> 1, AxesOrigin -> {0, 0, 0}], 
        Graphics3D[{Red, 
          PointSize[0.1], 
          Arrow[{$CellContext`o, $CellContext`x1$$ $CellContext`v11}]}, Axes -> 
         True, AspectRatio -> 1, AxesOrigin -> {0, 0, 0}], 
        Graphics3D[{Green, 
          PointSize[0.1], 
          
          Arrow[{$CellContext`x1$$ $CellContext`v11, $CellContext`x1$$ \
$CellContext`v11 + $CellContext`x2$$ $CellContext`v12}]}, Axes -> True, 
         AspectRatio -> 1, AxesOrigin -> {0, 0, 0}], 
        Graphics3D[{Blue, 
          PointSize[0.1], 
          
          Arrow[{$CellContext`x1$$ $CellContext`v11 + $CellContext`x2$$ \
$CellContext`v12, $CellContext`x1$$ $CellContext`v11 + $CellContext`x2$$ \
$CellContext`v12 + $CellContext`x3$$ $CellContext`v13}]}, Axes -> True, 
         AspectRatio -> 1, AxesOrigin -> {0, 0, 0}]], 
      "Specifications" :> {{$CellContext`x1$$, -100, 
         100}, {$CellContext`x2$$, -100, 100}, {$CellContext`x3$$, -100, 
         100}}, "Options" :> {}, "DefaultOptions" :> {}],
     ImageSizeCache->{411., {251., 256.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    Initialization:>({$CellContext`o = {0, 0, 0}, $CellContext`v14 = {4, 0, 
        1}, $CellContext`v11 = {1, 3, 1}, $CellContext`v12 = {5, 1, 
        9}, $CellContext`v13 = {4, 0, 6}}; Typeset`initDone$$ = True),
    SynchronousInitialization->True,
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{3.6665398162682524`*^9, 3.6665411131454387`*^9, 
  3.6665434795987043`*^9},
 TextJustification->1.]
}, {2}]],

Cell[TextData[{
 "Az egyenletrendszernek ekkor egy megold\[AAcute]sa van. Ennek az \
egyenletrendszernek a megold\[AAcute]sa ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "=1, ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "= \[Dash] 3, ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   FractionBox["9", "2"], TraditionalForm]]],
 ", mivel:"
}], "Text",
 CellChangeTimes->{{3.6665402848290615`*^9, 3.6665403378770957`*^9}, {
  3.6665435324999714`*^9, 3.666543532828193*^9}, {3.666545075793089*^9, 
  3.666545084245572*^9}, {3.6665451205216475`*^9, 3.66654517807994*^9}},
 TextJustification->1.],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"LinearSolve", "[", 
  RowBox[{
   RowBox[{"(", GridBox[{
      {"1", "5", "4"},
      {"3", "1", "0"},
      {"1", "9", "6"}
     }], ")"}], ",", 
   RowBox[{"{", 
    RowBox[{"4", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 TextJustification->1.],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"1", ",", 
   RowBox[{"-", "3"}], ",", 
   FractionBox["9", "2"]}], "}"}]], "Output",
 CellChangeTimes->{3.6665385352121363`*^9},
 TextJustification->1.]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
2. eset: A f\[UDoubleDot]ggetlen egyenletek sz\[AAcute]ma 1-gyel kisebb, mint \
a v\[AAcute]ltoz\[OAcute]k sz\[AAcute]ma: 2 f\[UDoubleDot]ggetlen egyenlet, 3 \
v\[AAcute]ltoz\[OAcute]\
\>", "Subsubsection",
 CellChangeTimes->{{3.6665404679615364`*^9, 3.6665405001913795`*^9}, {
  3.6665405660161448`*^9, 3.666540566970199*^9}, {3.6665414297315464`*^9, 
  3.666541431841667*^9}},
 TextJustification->1.,
 FontWeight->"Bold",
 FontSlant->"Italic"],

Cell["\<\
Ekkor p\[EAcute]ld\[AAcute]ul az egyik egyenlet egy m\[AAcute]sik egyenletnek \
a sz\[AAcute]mszorosa.

N\[EAcute]zz\[UDoubleDot]nk erre is egy p\[EAcute]ld\[AAcute]t:\
\>", "Text",
 CellChangeTimes->{{3.6665405722305*^9, 3.66654060160218*^9}},
 TextJustification->1.],

Cell[TextData[{
 "\t1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+5\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+3\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=28\n\t3\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+0\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0\n\t6\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+2\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+0\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0"
}], "Text",
 CellChangeTimes->{{3.6665406117137585`*^9, 3.666540613280848*^9}, {
  3.666540658670444*^9, 3.666540670765136*^9}, {3.6665408808701534`*^9, 
  3.6665408836403117`*^9}, {3.666540945560853*^9, 3.6665409479879923`*^9}},
 TextJustification->1.],

Cell["\<\
Itt a harmadik egyenlet a m\[AAcute]sodik egyenlet k\[EAcute]tszerese.

N\[EAcute]zz\[UDoubleDot]k ezt \[AAcute]br\[AAcute]val. A feldat megint \
ugyanaz, a k\[EAcute]k vektor v\[EAcute]gpontja a lila vektor \
v\[EAcute]gpontj\[AAcute]val kell egybeessen.\
\>", "Text",
 CellChangeTimes->{{3.6665408959820175`*^9, 3.666540939176488*^9}, {
  3.6665411376528406`*^9, 3.666541168265591*^9}, {3.6665435849169226`*^9, 
  3.6665435855433407`*^9}},
 TextJustification->1.],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"v21", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "3", ",", "6"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"v22", "=", 
   RowBox[{"{", 
    RowBox[{"5", ",", "1", ",", "2"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"v23", "=", 
   RowBox[{"{", 
    RowBox[{"3", ",", "0", ",", "0"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"v24", "=", 
   RowBox[{"{", 
    RowBox[{"28", ",", "0", ",", "0"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"Manipulate", "[", 
  RowBox[{
   RowBox[{"Show", "[", 
    RowBox[{
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Purple", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{"o", ",", "v24"}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Red", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{"o", ",", 
            RowBox[{"x1", "*", "v21"}]}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Green", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"x1", "*", "v21"}], ",", 
            RowBox[{
             RowBox[{"x1", "*", "v21"}], "+", 
             RowBox[{"x2", "*", "v22"}]}]}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Blue", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{
             RowBox[{"x1", "*", "v21"}], "+", 
             RowBox[{"x2", "*", "v22"}]}], ",", 
            RowBox[{
             RowBox[{"x1", "*", "v21"}], "+", 
             RowBox[{"x2", "*", "v22"}], "+", 
             RowBox[{"x3", "*", "v23"}]}]}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x1", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x2", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x3", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"SaveDefinitions", "\[Rule]", "True"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.6665409613997593`*^9, 3.666540985578142*^9}},
 TextJustification->1.],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`x1$$ = -100., $CellContext`x2$$ = -100, \
$CellContext`x3$$ = -100, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, 
    Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 
    1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{
      Hold[$CellContext`x1$$], -100, 100}, {
      Hold[$CellContext`x2$$], -100, 100}, {
      Hold[$CellContext`x3$$], -100, 100}}, Typeset`size$$ = {
    360., {178., 182.}}, Typeset`update$$ = 0, Typeset`initDone$$, 
    Typeset`skipInitDone$$ = False, $CellContext`x1$2707$$ = 
    0, $CellContext`x2$2708$$ = 0, $CellContext`x3$2709$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`x1$$ = -100, $CellContext`x2$$ = -100, \
$CellContext`x3$$ = -100}, "ControllerVariables" :> {
        Hold[$CellContext`x1$$, $CellContext`x1$2707$$, 0], 
        Hold[$CellContext`x2$$, $CellContext`x2$2708$$, 0], 
        Hold[$CellContext`x3$$, $CellContext`x3$2709$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, "Body" :> Show[
        Graphics3D[{Purple, 
          PointSize[0.1], 
          Arrow[{$CellContext`o, $CellContext`v24}]}, Axes -> True, 
         AspectRatio -> 1, AxesOrigin -> {0, 0, 0}], 
        Graphics3D[{Red, 
          PointSize[0.1], 
          Arrow[{$CellContext`o, $CellContext`x1$$ $CellContext`v21}]}, Axes -> 
         True, AspectRatio -> 1, AxesOrigin -> {0, 0, 0}], 
        Graphics3D[{Green, 
          PointSize[0.1], 
          
          Arrow[{$CellContext`x1$$ $CellContext`v21, $CellContext`x1$$ \
$CellContext`v21 + $CellContext`x2$$ $CellContext`v22}]}, Axes -> True, 
         AspectRatio -> 1, AxesOrigin -> {0, 0, 0}], 
        Graphics3D[{Blue, 
          PointSize[0.1], 
          
          Arrow[{$CellContext`x1$$ $CellContext`v21 + $CellContext`x2$$ \
$CellContext`v22, $CellContext`x1$$ $CellContext`v21 + $CellContext`x2$$ \
$CellContext`v22 + $CellContext`x3$$ $CellContext`v23}]}, Axes -> True, 
         AspectRatio -> 1, AxesOrigin -> {0, 0, 0}]], 
      "Specifications" :> {{$CellContext`x1$$, -100, 
         100}, {$CellContext`x2$$, -100, 100}, {$CellContext`x3$$, -100, 
         100}}, "Options" :> {}, "DefaultOptions" :> {}],
     ImageSizeCache->{411., {251., 256.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    Initialization:>({$CellContext`o = {0, 0, 0}, $CellContext`v24 = {28, 0, 
        0}, $CellContext`v21 = {1, 3, 6}, $CellContext`v22 = {5, 1, 
        2}, $CellContext`v23 = {3, 0, 0}}; Typeset`initDone$$ = True),
    SynchronousInitialization->True,
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{3.6665410207911563`*^9, 3.6665435419142485`*^9},
 TextJustification->1.]
}, {2}]],

Cell[TextData[{
 "A helyes be\[AAcute]ll\[IAcute]t\[AAcute]s: ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  RowBox[{
   FractionBox[
    RowBox[{"3", "\[CenterDot]", 
     FormBox[
      SubscriptBox["x", "3"],
      TraditionalForm]}], "14"], "-", "2"}]],
  CellChangeTimes->{{3.6665312915390377`*^9, 3.666531316900946*^9}, 
    3.6665334885965223`*^9}],
 ", ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  RowBox[{"6", "-", 
   FractionBox[
    RowBox[{"9", "\[CenterDot]", 
     FormBox[
      SubscriptBox["x", "3"],
      TraditionalForm]}], "14"]}]],
  CellChangeTimes->{{3.6665312915390377`*^9, 3.666531316900946*^9}, 
    3.6665334885965223`*^9}],
 ", ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "; ahol ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 " tetsz\[ODoubleAcute]leges val\[OAcute]s sz\[AAcute]m lehet.\n\
L\[AAcute]that\[OAcute], hogy mivel az ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 " b\[AAcute]rmi lehet, \[IAcute]gy v\[EAcute]gtelen sok megold\[AAcute]sa \
van az egyenletrendszernek. Ilyen esetben az ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "-at szabad v\[AAcute]ltoz\[OAcute]nak nevezz\[UDoubleDot]k.\nEz azt \
jelenti, hogy ha v\[AAcute]lasztunk egy tetsz\[ODoubleAcute]leges ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 " val\[OAcute]s sz\[AAcute]mot, \[EAcute]s azt behelyettes\[IAcute]tj\
\[UDoubleDot]k a megadott k\[EAcute]pletekbe, amivel ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "-et, \[EAcute]s ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "-t kisz\[AAcute]molhatjuk, akkor ha ezt a 3 sz\[AAcute]mot be\[AAcute]ll\
\[IAcute]tjuk az \[AAcute]br\[AAcute]n, akkor a k\[EAcute]k vektor \
v\[EAcute]gpontja t\[EAcute]nyleg a lila vektor v\[EAcute]gpontj\[AAcute]ba \
mutat."
}], "Text",
 CellChangeTimes->{{3.6665412143412266`*^9, 3.666541295071844*^9}, {
  3.666541778832514*^9, 3.6665417892491093`*^9}, {3.6665451914287033`*^9, 
  3.6665452806348057`*^9}, {3.6665454892727385`*^9, 3.6665455902085123`*^9}},
 TextJustification->1.]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
3. eset: A f\[UDoubleDot]ggetlen egyenletek sz\[AAcute]ma 2-vel kisebb, mint \
a v\[AAcute]ltoz\[OAcute]k sz\[AAcute]ma: 1 f\[UDoubleDot]ggetlen egyenlet, 3 \
v\[AAcute]ltoz\[OAcute]\
\>", "Subsubsection",
 CellChangeTimes->{{3.6665414061491976`*^9, 3.6665414374949903`*^9}},
 TextJustification->1.,
 FontWeight->"Bold",
 FontSlant->"Italic"],

Cell["\<\
Ekkor mindh\[AAcute]rom egyenlet egym\[AAcute]s sz\[AAcute]mszorosa. N\
\[EAcute]zz\[UDoubleDot]nk erre is egy p\[EAcute]ld\[AAcute]t:\
\>", "Text",
 CellChangeTimes->{{3.66654144186024*^9, 3.6665414637254906`*^9}},
 TextJustification->1.],

Cell[TextData[{
 "\t1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+5\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+2\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=4\n\t3\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+15\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+6\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=12\n\t6\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+30\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+12\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=24"
}], "Text",
 CellChangeTimes->{{3.6665414713019238`*^9, 3.666541509434105*^9}},
 TextJustification->1.],

Cell["\<\
L\[AAcute]that\[OAcute], hogy a m\[AAcute]sodik egyenlet az \
els\[ODoubleAcute]nek h\[AAcute]romszorosa, a harmadik egyenlet pedig az els\
\[ODoubleAcute]nek hatszorosa.
N\[EAcute]zz\[UDoubleDot]k most is az \[AAcute]br\[AAcute]t. A feladat \
ugyanaz, mint el\[ODoubleAcute]z\[ODoubleAcute]leg.\
\>", "Text",
 CellChangeTimes->{{3.66654155777687*^9, 3.6665416340142307`*^9}},
 TextJustification->1.],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"v31", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "3", ",", "6"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"v32", "=", 
   RowBox[{"{", 
    RowBox[{"5", ",", "15", ",", "30"}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"v33", "=", 
   RowBox[{"{", 
    RowBox[{"2", ",", "6", ",", "12"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"v34", "=", 
   RowBox[{"{", 
    RowBox[{"4", ",", "12", ",", "24"}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"Manipulate", "[", 
  RowBox[{
   RowBox[{"Show", "[", 
    RowBox[{
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Purple", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{"o", ",", "v34"}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Red", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{"o", ",", 
            RowBox[{"x1", "*", "v31"}]}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Green", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"x1", "*", "v31"}], ",", 
            RowBox[{
             RowBox[{"x1", "*", "v31"}], "+", 
             RowBox[{"x2", "*", "v32"}]}]}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Blue", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{
             RowBox[{"x1", "*", "v31"}], "+", 
             RowBox[{"x2", "*", "v32"}]}], ",", 
            RowBox[{
             RowBox[{"x1", "*", "v31"}], "+", 
             RowBox[{"x2", "*", "v32"}], "+", 
             RowBox[{"x3", "*", "v33"}]}]}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x1", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x2", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x3", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"SaveDefinitions", "\[Rule]", "True"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.6665415203017263`*^9, 3.6665415426530046`*^9}},
 TextJustification->1.],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`x1$$ = -100, $CellContext`x2$$ = -100, \
$CellContext`x3$$ = -100, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, 
    Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 
    1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{
      Hold[$CellContext`x1$$], -100, 100}, {
      Hold[$CellContext`x2$$], -100, 100}, {
      Hold[$CellContext`x3$$], -100, 100}}, Typeset`size$$ = {
    360., {182., 185.}}, Typeset`update$$ = 0, Typeset`initDone$$, 
    Typeset`skipInitDone$$ = False, $CellContext`x1$2814$$ = 
    0, $CellContext`x2$2815$$ = 0, $CellContext`x3$2816$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`x1$$ = -100, $CellContext`x2$$ = -100, \
$CellContext`x3$$ = -100}, "ControllerVariables" :> {
        Hold[$CellContext`x1$$, $CellContext`x1$2814$$, 0], 
        Hold[$CellContext`x2$$, $CellContext`x2$2815$$, 0], 
        Hold[$CellContext`x3$$, $CellContext`x3$2816$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, "Body" :> Show[
        Graphics3D[{Purple, 
          PointSize[0.1], 
          Arrow[{$CellContext`o, $CellContext`v34}]}, Axes -> True, 
         AspectRatio -> 1, AxesOrigin -> {0, 0, 0}], 
        Graphics3D[{Red, 
          PointSize[0.1], 
          Arrow[{$CellContext`o, $CellContext`x1$$ $CellContext`v31}]}, Axes -> 
         True, AspectRatio -> 1, AxesOrigin -> {0, 0, 0}], 
        Graphics3D[{Green, 
          PointSize[0.1], 
          
          Arrow[{$CellContext`x1$$ $CellContext`v31, $CellContext`x1$$ \
$CellContext`v31 + $CellContext`x2$$ $CellContext`v32}]}, Axes -> True, 
         AspectRatio -> 1, AxesOrigin -> {0, 0, 0}], 
        Graphics3D[{Blue, 
          PointSize[0.1], 
          
          Arrow[{$CellContext`x1$$ $CellContext`v31 + $CellContext`x2$$ \
$CellContext`v32, $CellContext`x1$$ $CellContext`v31 + $CellContext`x2$$ \
$CellContext`v32 + $CellContext`x3$$ $CellContext`v33}]}, Axes -> True, 
         AspectRatio -> 1, AxesOrigin -> {0, 0, 0}]], 
      "Specifications" :> {{$CellContext`x1$$, -100, 
         100}, {$CellContext`x2$$, -100, 100}, {$CellContext`x3$$, -100, 
         100}}, "Options" :> {}, "DefaultOptions" :> {}],
     ImageSizeCache->{411., {255., 260.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    Initialization:>({$CellContext`o = {0, 0, 0}, $CellContext`v34 = {4, 12, 
        24}, $CellContext`v31 = {1, 3, 6}, $CellContext`v32 = {5, 15, 
        30}, $CellContext`v33 = {2, 6, 12}}; Typeset`initDone$$ = True),
    SynchronousInitialization->True,
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{3.66654154571218*^9, 3.666543647449604*^9},
 TextJustification->1.]
}, {2}]],

Cell[TextData[{
 "A helyes be\[AAcute]ll\[IAcute]t\[AAcute]s: ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "=4\[Dash]5\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "\[Dash]2\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 ", ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 ", ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 " ahol ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 " \[EAcute]s ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 " tetsz\[ODoubleAcute]leges val\[OAcute]s sz\[AAcute]m.\nL\[AAcute]that\
\[OAcute], hogy az egyenletrendszernek ebben az esetben is v\[EAcute]gtelen \
sok megold\[AAcute]sa van, tov\[AAcute]bb\[AAcute] k\[EAcute]t szabad v\
\[AAcute]ltoz\[OAcute]ja.\nEz azt jelenti, hogy ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 ", \[EAcute]s ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 " hely\[EAcute]re is b\[AAcute]rmilyen val\[OAcute]s sz\[AAcute]mot \
behelyettes\[IAcute]thet\[UDoubleDot]nk, \[EAcute]s \[IAcute]gy ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "-et kisz\[AAcute]molva be\[AAcute]ll\[IAcute]tjuk a megfelel\[ODoubleAcute] \
sz\[AAcute]mokat az \[AAcute]br\[AAcute]n, akkor a k\[EAcute]k vektor v\
\[EAcute]gpontja a lila vektor v\[EAcute]gpontj\[AAcute]ba fog mutatni."
}], "Text",
 CellChangeTimes->{{3.6665416813379374`*^9, 3.6665417702750244`*^9}, {
  3.666545298827846*^9, 3.6665453570571766`*^9}, {3.6665455946767673`*^9, 
  3.6665456801596565`*^9}},
 TextJustification->1.],

Cell[BoxData[
 StyleBox[
  RowBox[{
  "Homog\[EAcute]n", " ", "line\[AAcute]ris", " ", "egyenletrendszerek"}], 
  "Section",
  FontWeight->"Plain"]], "Input",
 CellChangeTimes->{{3.6665390303348618`*^9, 3.666539030379862*^9}, {
  3.666539064896911*^9, 3.666539073763926*^9}},
 TextJustification->1.,
 FontSlant->"Italic"],

Cell["\<\
T\[EAcute]rj\[UDoubleDot]nk r\[AAcute] a homog\[EAcute]n line\[AAcute]ris \
egyenletrendszerekre. Egy ilyen t\[IAcute]pus\[UAcute], 3 v\[AAcute]ltoz\
\[OAcute]s line\[AAcute]ris egyenletrendszer a k\[ODoubleDot]vetkez\
\[ODoubleAcute] \[AAcute]ltal\[AAcute]nos alakban \[IAcute]rhat\[OAcute] fel:\
\>", "Text",
 CellChangeTimes->{{3.6665418176967363`*^9, 3.6665418674025793`*^9}},
 TextJustification->1.],

Cell[TextData[{
 "\t",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "11"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "12"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "13"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox["0", TraditionalForm]]],
 "\n\t",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "21"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "22"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "23"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox["0", TraditionalForm]]],
 "\n\t",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "31"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "32"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "33"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox["0", TraditionalForm]]],
 "\n\t\[VerticalEllipsis]\n\t",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "m1"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "m2"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+",
 Cell[BoxData[
  FormBox[
   SubscriptBox["a", "m3"], TraditionalForm]]],
 "\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox["0", TraditionalForm]]]
}], "Text",
 CellChangeTimes->{{3.666541885559618*^9, 3.6665418959032097`*^9}},
 TextJustification->1.],

Cell["K\[EAcute]t esetet k\[UDoubleDot]l\[ODoubleDot]nb\[ODoubleDot]ztet\
\[UDoubleDot]nk meg ilyenkor.", "Text",
 CellChangeTimes->{{3.6665419080679054`*^9, 3.6665419187775183`*^9}},
 TextJustification->1.]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Csak a trivi\[AAcute]lis megold\[AAcute]s megold\
\[AAcute]sa az egyenletrendszernek", "Subsection"]], "Subsubsection",
 CellChangeTimes->{{3.666541926610966*^9, 3.6665419371055665`*^9}},
 TextJustification->1.,
 FontWeight->"Bold",
 FontSlant->"Italic"],

Cell[TextData[{
 "Ez azt jelenti, hogy az egyenletnek csak az ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0 a megold\[AAcute]sa. K\[ODoubleDot]nny\[UDoubleAcute] \
v\[EAcute]giggondolni, hogy ez a megold\[AAcute]s az \[ODoubleDot]sszes homog\
\[EAcute]n line\[AAcute]ris egyenletrendszernek megold\[AAcute]sa.\n\nN\
\[EAcute]zz\[UDoubleDot]nk meg egy ilyen 3 v\[AAcute]ltoz\[OAcute]s \
egyenletrendszert."
}], "Text",
 CellChangeTimes->{{3.6665420531782055`*^9, 3.6665420937095237`*^9}, {
   3.666542152339877*^9, 3.666542176356251*^9}, 3.6665422079790597`*^9, {
   3.666545366474715*^9, 3.666545376438285*^9}},
 TextJustification->1.],

Cell[TextData[{
 "\t1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+5\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+4\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0\n\t3\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+0\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0\n\t1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+9\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+6\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0"
}], "Text",
 CellChangeTimes->{{3.6665422043378515`*^9, 3.6665422065959806`*^9}, {
  3.666542244161129*^9, 3.666542269074554*^9}},
 TextJustification->1.],

Cell["\<\
N\[EAcute]zz\[UDoubleDot]k meg most is az \[AAcute]br\[AAcute]t. Annyiban v\
\[AAcute]ltozik most a feladat, hogy minden esetben az eddigi lila vektor a \
nullvektor lesz, \[IAcute]gy a k\[EAcute]k vektornak most az orig\[OAcute]ba \
kell mutatnia.\
\>", "Text",
 CellChangeTimes->{{3.6665422173265944`*^9, 3.6665422289042563`*^9}, {
  3.6665422719307175`*^9, 3.666542310210907*^9}, {3.6665437666080427`*^9, 
  3.6665437876020446`*^9}},
 TextJustification->1.],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"v41", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "3", ",", "1"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"v42", "=", 
   RowBox[{"{", 
    RowBox[{"5", ",", "1", ",", "9"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"v43", "=", 
   RowBox[{"{", 
    RowBox[{"4", ",", "0", ",", "6"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"Manipulate", "[", 
  RowBox[{
   RowBox[{"Show", "[", 
    RowBox[{
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Red", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{"o", ",", 
            RowBox[{"x1", "*", "v41"}]}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Green", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"x1", "*", "v41"}], ",", 
            RowBox[{
             RowBox[{"x1", "*", "v41"}], "+", 
             RowBox[{"x2", "*", "v42"}]}]}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Blue", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{
             RowBox[{"x1", "*", "v41"}], "+", 
             RowBox[{"x2", "*", "v42"}]}], ",", 
            RowBox[{
             RowBox[{"x1", "*", "v41"}], "+", 
             RowBox[{"x2", "*", "v42"}], "+", 
             RowBox[{"x3", "*", "v43"}]}]}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x1", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x2", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x3", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"SaveDefinitions", "\[Rule]", "True"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.6665421229811983`*^9, 3.6665421437583866`*^9}},
 TextJustification->1.],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`x1$$ = -100, $CellContext`x2$$ = -100, \
$CellContext`x3$$ = -100, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, 
    Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 
    1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{
      Hold[$CellContext`x1$$], -100, 100}, {
      Hold[$CellContext`x2$$], -100, 100}, {
      Hold[$CellContext`x3$$], -100, 100}}, Typeset`size$$ = {
    360., {177., 181.}}, Typeset`update$$ = 0, Typeset`initDone$$, 
    Typeset`skipInitDone$$ = False, $CellContext`x1$2921$$ = 
    0, $CellContext`x2$2922$$ = 0, $CellContext`x3$2923$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`x1$$ = -100, $CellContext`x2$$ = -100, \
$CellContext`x3$$ = -100}, "ControllerVariables" :> {
        Hold[$CellContext`x1$$, $CellContext`x1$2921$$, 0], 
        Hold[$CellContext`x2$$, $CellContext`x2$2922$$, 0], 
        Hold[$CellContext`x3$$, $CellContext`x3$2923$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, "Body" :> Show[
        Graphics3D[{Red, 
          PointSize[0.1], 
          Arrow[{$CellContext`o, $CellContext`x1$$ $CellContext`v41}]}, Axes -> 
         True, AspectRatio -> 1, AxesOrigin -> {0, 0, 0}], 
        Graphics3D[{Green, 
          PointSize[0.1], 
          
          Arrow[{$CellContext`x1$$ $CellContext`v41, $CellContext`x1$$ \
$CellContext`v41 + $CellContext`x2$$ $CellContext`v42}]}, Axes -> True, 
         AspectRatio -> 1, AxesOrigin -> {0, 0, 0}], 
        Graphics3D[{Blue, 
          PointSize[0.1], 
          
          Arrow[{$CellContext`x1$$ $CellContext`v41 + $CellContext`x2$$ \
$CellContext`v42, $CellContext`x1$$ $CellContext`v41 + $CellContext`x2$$ \
$CellContext`v42 + $CellContext`x3$$ $CellContext`v43}]}, Axes -> True, 
         AspectRatio -> 1, AxesOrigin -> {0, 0, 0}]], 
      "Specifications" :> {{$CellContext`x1$$, -100, 
         100}, {$CellContext`x2$$, -100, 100}, {$CellContext`x3$$, -100, 
         100}}, "Options" :> {}, "DefaultOptions" :> {}],
     ImageSizeCache->{411., {250., 255.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    Initialization:>({$CellContext`o = {0, 0, 0}, $CellContext`v41 = {1, 3, 
        1}, $CellContext`v42 = {5, 1, 9}, $CellContext`v43 = {4, 0, 6}}; 
     Typeset`initDone$$ = True),
    SynchronousInitialization->True,
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{3.6665421454044805`*^9, 3.6665437474342604`*^9},
 TextJustification->1.]
}, {2}]],

Cell[TextData[{
 "L\[AAcute]that\[OAcute], hogy b\[AAcute]rhogy is \
pr\[OAcute]b\[AAcute]lkozunk a sz\[AAcute]mok megv\[AAcute]laszt\[AAcute]s\
\[AAcute]val, csak ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0 lesz a j\[OAcute] megold\[AAcute]s, azaz csak ebben az esetben mutat a k\
\[EAcute]k vektor az orig\[OAcute]ba."
}], "Text",
 CellChangeTimes->{{3.666542339090559*^9, 3.666542353062358*^9}, 
   3.666543826778156*^9, {3.666545386276848*^9, 3.666545393522262*^9}, {
   3.6665456879871044`*^9, 3.666545708244263*^9}, {3.666545802142634*^9, 
   3.6665458119291935`*^9}},
 TextJustification->1.]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["   Van nem trivi\[AAcute]lis megold\[AAcute]sa is az \
egyenletrendszernek", "Subsection",
 CellChangeTimes->{{3.6665420249915934`*^9, 3.6665420342511225`*^9}},
 TextJustification->1.,
 FontWeight->"Bold",
 FontSlant->"Italic"],

Cell["\<\
N\[EAcute]zz\[UDoubleDot]k most azokat az eseteket, amikor a \
trivi\[AAcute]lis megold\[AAcute]son k\[IAcute]v\[UDoubleDot]l m\[AAcute]s \
megold\[AAcute]sa is van az egyenletrendszernek. Vegy\[UDoubleDot]nk egy \
ilyen egyenletrendszert.\
\>", "Text",
 CellChangeTimes->{{3.666542389625449*^9, 3.6665424453506365`*^9}, 
   3.666543845820854*^9},
 TextJustification->1.],

Cell[TextData[{
 "\t1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+2\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0\n\t0\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+3\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+2\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0\n\t5\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+4\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0"
}], "Text",
 CellChangeTimes->{{3.6665424539201264`*^9, 3.666542485736946*^9}},
 TextJustification->1.],

Cell["\<\
Vizsg\[AAcute]ljuk a hozz\[AAcute] tartoz\[OAcute] \[AAcute]br\[AAcute]t. \
Ugyan\[UAcute]gy az a feladat, hogy a k\[EAcute]k vektor az orig\[OAcute]ba \
mutasson.\
\>", "Text",
 CellChangeTimes->{{3.6665424909372435`*^9, 3.6665425223160386`*^9}},
 TextJustification->1.],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"v51", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "0", ",", "5"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"v52", "=", 
   RowBox[{"{", 
    RowBox[{"2", ",", "3", ",", "4"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"v53", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "2", ",", "1"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"Manipulate", "[", 
  RowBox[{
   RowBox[{"Show", "[", 
    RowBox[{
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Red", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{"o", ",", 
            RowBox[{"x1", "*", "v51"}]}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Green", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"x1", "*", "v51"}], ",", 
            RowBox[{
             RowBox[{"x1", "*", "v51"}], "+", 
             RowBox[{"x2", "*", "v52"}]}]}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}], ",", 
     RowBox[{"Graphics3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"Blue", ",", 
         RowBox[{"PointSize", "[", "0.1", "]"}], ",", 
         RowBox[{"Arrow", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{
             RowBox[{"x1", "*", "v51"}], "+", 
             RowBox[{"x2", "*", "v52"}]}], ",", 
            RowBox[{
             RowBox[{"x1", "*", "v51"}], "+", 
             RowBox[{"x2", "*", "v52"}], "+", 
             RowBox[{"x3", "*", "v53"}]}]}], "}"}], "]"}]}], "}"}], ",", 
       RowBox[{"Axes", "\[Rule]", "True"}], ",", 
       RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0", ",", "0"}], "}"}]}]}], "]"}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x1", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x2", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"x3", ",", 
     RowBox[{"-", "100"}], ",", "100"}], "}"}], ",", 
   RowBox[{"SaveDefinitions", "\[Rule]", "True"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.6665425356758027`*^9, 3.6665425544158745`*^9}},
 TextJustification->1.],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`x1$$ = -100, $CellContext`x2$$ = -100, \
$CellContext`x3$$ = -100, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, 
    Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 
    1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{
      Hold[$CellContext`x1$$], -100, 100}, {
      Hold[$CellContext`x2$$], -100, 100}, {
      Hold[$CellContext`x3$$], -100, 100}}, Typeset`size$$ = {
    360., {183., 186.}}, Typeset`update$$ = 0, Typeset`initDone$$, 
    Typeset`skipInitDone$$ = False, $CellContext`x1$3018$$ = 
    0, $CellContext`x2$3019$$ = 0, $CellContext`x3$3020$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`x1$$ = -100, $CellContext`x2$$ = -100, \
$CellContext`x3$$ = -100}, "ControllerVariables" :> {
        Hold[$CellContext`x1$$, $CellContext`x1$3018$$, 0], 
        Hold[$CellContext`x2$$, $CellContext`x2$3019$$, 0], 
        Hold[$CellContext`x3$$, $CellContext`x3$3020$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, "Body" :> Show[
        Graphics3D[{Red, 
          PointSize[0.1], 
          Arrow[{$CellContext`o, $CellContext`x1$$ $CellContext`v51}]}, Axes -> 
         True, AspectRatio -> 1, AxesOrigin -> {0, 0, 0}], 
        Graphics3D[{Green, 
          PointSize[0.1], 
          
          Arrow[{$CellContext`x1$$ $CellContext`v51, $CellContext`x1$$ \
$CellContext`v51 + $CellContext`x2$$ $CellContext`v52}]}, Axes -> True, 
         AspectRatio -> 1, AxesOrigin -> {0, 0, 0}], 
        Graphics3D[{Blue, 
          PointSize[0.1], 
          
          Arrow[{$CellContext`x1$$ $CellContext`v51 + $CellContext`x2$$ \
$CellContext`v52, $CellContext`x1$$ $CellContext`v51 + $CellContext`x2$$ \
$CellContext`v52 + $CellContext`x3$$ $CellContext`v53}]}, Axes -> True, 
         AspectRatio -> 1, AxesOrigin -> {0, 0, 0}]], 
      "Specifications" :> {{$CellContext`x1$$, -100, 
         100}, {$CellContext`x2$$, -100, 100}, {$CellContext`x3$$, -100, 
         100}}, "Options" :> {}, "DefaultOptions" :> {}],
     ImageSizeCache->{411., {256., 261.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    Initialization:>({$CellContext`o = {0, 0, 0}, $CellContext`v51 = {1, 0, 
        5}, $CellContext`v52 = {2, 3, 4}, $CellContext`v53 = {1, 2, 1}}; 
     Typeset`initDone$$ = True),
    SynchronousInitialization->True,
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{3.6665425557529507`*^9, 3.6665438798635464`*^9},
 TextJustification->1.]
}, {2}]],

Cell[TextData[{
 "L\[AAcute]that\[OAcute], hogy az ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0 megold\[AAcute]sa az egyenletrendszernek.\nTov\[AAcute]bb\[AAcute] a k\
\[ODoubleDot]vetkez\[ODoubleAcute]k is megold\[AAcute]sok: ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  RowBox[{" ", 
   RowBox[{
    RowBox[{"-", 
     FractionBox["1", "2"]}], " ", "\[CenterDot]", 
    FormBox[
     SubscriptBox["x", "2"],
     TraditionalForm]}]}]],
  CellChangeTimes->{{3.6665312915390377`*^9, 3.666531316900946*^9}, 
    3.6665334885965223`*^9}],
 ", ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 ", ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=",
 Cell[BoxData[
  RowBox[{" ", 
   RowBox[{
    RowBox[{"-", 
     FractionBox["3", "2"]}], " ", "\[CenterDot]", 
    FormBox[
     SubscriptBox["x", "2"],
     TraditionalForm]}]}]],
  CellChangeTimes->{{3.6665312915390377`*^9, 3.666531316900946*^9}, 
    3.6665334885965223`*^9}],
 "; ahol ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 " tetsz\[ODoubleAcute]leges val\[OAcute]s sz\[AAcute]m. Teh\[AAcute]t v\
\[EAcute]gtelen sok megold\[AAcute]sa van az egyenletrendszernek, \[EAcute]s \
egy szabad v\[AAcute]ltoz\[OAcute]ja.\nEz most azt jelenti, hogy ha ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "-nek v\[AAcute]lasztunk egy tetsz\[ODoubleAcute]leges val\[OAcute]s sz\
\[AAcute]mot, \[EAcute]s ebb\[ODoubleAcute]l ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "-t \[EAcute]s ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "-t kisz\[AAcute]moljuk, \[EAcute]s ezeket a sz\[AAcute]mokat be\[AAcute]ll\
\[IAcute]tjuk az \[AAcute]br\[AAcute]n, akkor a k\[EAcute]k vektor \
v\[EAcute]gpontja az orig\[OAcute]ban lesz."
}], "Text",
 CellChangeTimes->{{3.6665425647474656`*^9, 3.6665426836892686`*^9}, {
  3.666545399384598*^9, 3.6665454710626974`*^9}, {3.666545717510793*^9, 
  3.666545824873934*^9}},
 TextJustification->1.]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Grafikus \[AAcute]br\[AAcute]zol\[AAcute]s II.",
 FontWeight->"Bold",
 FontSlant->"Italic"]], "Section",
 CellChangeTimes->{{3.6672207582084937`*^9, 3.667220765100888*^9}}],

Cell["\<\
Egy m\[AAcute]sik lehets\[EAcute]ges grafikus megold\[AAcute]sa az \
egyenletrendszernek, ha a h\[AAcute]rom ismeretlenes egyenleteket mint s\
\[IAcute]kokat \[AAcute]br\[AAcute]zoljuk. P\[EAcute]ld\[AAcute]ul, ha a h\
\[AAcute]rom egyenlet h\[AAcute]rom s\[IAcute]k \[AAcute]ltal\[AAcute]nos \
egyenlet\[EAcute]t adja meg, akkor az egyenletrendszer megold\[AAcute]sai \
azok a pontok, amelyek mind a h\[AAcute]rom s\[IAcute]kban benne vannak.
Egy ilyen egyenletrendszernek lehet pontosan egy megold\[AAcute]sa \
(h\[AAcute]rom \[AAcute]ltal\[AAcute]nos helyzet\[UDoubleAcute] s\[IAcute]k \
eset\[EAcute]n), v\[EAcute]gtelen sok megold\[AAcute]sa \
(p\[EAcute]ld\[AAcute]ul egy egyenes minden pontja), de lehet, hogy egy \
megold\[AAcute]s sincs (p\[EAcute]ld\[AAcute]ul ha k\[EAcute]t s\[IAcute]k p\
\[AAcute]rhuzamos a h\[AAcute]rom k\[ODoubleDot]z\[UDoubleDot]l).

N\[EAcute]zz\[UDoubleDot]k ezt meg az eddigi p\[EAcute]ld\[AAcute]kkal:\
\>", "Text",
 CellChangeTimes->{{3.667220845528488*^9, 3.6672209145754375`*^9}, {
   3.667221709006876*^9, 3.667221735215375*^9}, {3.667221810217665*^9, 
   3.667221850393963*^9}, 3.667233802905718*^9, {3.667233985300388*^9, 
   3.6672339968320804`*^9}, {3.6672340647473855`*^9, 3.667234066740715*^9}},
 TextJustification->1.],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Inhomog\[EAcute]n line\[AAcute]ris \
egyenletrendszerek", "Section"]], "Subsection",
 CellChangeTimes->{3.6672218764354525`*^9}],

Cell[CellGroupData[{

Cell["\<\
1. eset: A f\[UDoubleDot]ggetlen egyenletek sz\[AAcute]ma \[EAcute]s a v\
\[AAcute]ltoz\[OAcute]k sz\[AAcute]ma egyenl\[ODoubleAcute]: 3 \
f\[UDoubleDot]ggetlen egyenlet, 3 v\[AAcute]ltoz\[OAcute]\
\>", "Subsubsection",
 CellChangeTimes->{3.667221961342309*^9}],

Cell[CellGroupData[{

Cell[TextData[{
 "\t1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+5\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+4\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=4\n\t3\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+0\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0\n\t1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+9\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+6\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=1"
}], "Text",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6672219928701124`*^9, 3.6672219969843473`*^9}, 
   3.667222130939009*^9}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"n11", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "5", ",", "4"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sik11", "=", 
   RowBox[{"n11", ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], ")"}]}]}], ";"}]}], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6671366808089375`*^9, 3.667136682584039*^9}, {
   3.6671392786087813`*^9, 3.6671392811124535`*^9}, 3.667222061275025*^9, 
   3.66722211434006*^9}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"n12", "=", 
   RowBox[{"{", 
    RowBox[{"3", ",", "1", ",", "0"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sik12", "=", 
   RowBox[{"n12", ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], ")"}]}]}], ";"}]}], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6671366843091373`*^9, 3.6671367006360717`*^9}, {
   3.6671392832288656`*^9, 3.667139288901652*^9}, 3.667222064047183*^9, 
   3.66722211434006*^9}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"n13", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "9", ",", "6"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sik13", "=", 
   RowBox[{"n13", ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], ")"}]}]}], ";"}]}], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6671367147988815`*^9, 3.6671367197911673`*^9}, {
   3.667139290518731*^9, 3.66713929274922*^9}, 3.6672220684554358`*^9, 
   3.6672221143410597`*^9}]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"ContourPlot3D", "[", 
    RowBox[{
     RowBox[{"sik11", "\[Equal]", "4"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"Mesh", "\[Rule]", "None"}]}], "]"}], ",", " ", 
   RowBox[{"ContourPlot3D", "[", 
    RowBox[{
     RowBox[{"sik12", "\[Equal]", "0"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"Mesh", "\[Rule]", "None"}]}], "]"}], ",", " ", 
   RowBox[{"ContourPlot3D", "[", 
    RowBox[{
     RowBox[{"sik13", "\[Equal]", "1"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"Mesh", "\[Rule]", "None"}]}], "]"}], ",", " ", 
   RowBox[{"Graphics3D", "[", 
    RowBox[{"{", 
     RowBox[{"Red", ",", 
      RowBox[{"PointSize", "[", "0.05", "]"}], ",", 
      RowBox[{"Point", "[", 
       RowBox[{"{", 
        RowBox[{"1", ",", 
         RowBox[{"-", "3"}], ",", "4.5"}], "}"}], "]"}]}], "}"}], "]"}], ",", 
   RowBox[{"AxesLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"x", ",", "y", ",", "z"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.667136754439149*^9, 3.6671367752563396`*^9}, {
  3.6671373840481606`*^9, 3.667137405438384*^9}, {3.6671376447290707`*^9, 
  3.667137674998802*^9}, {3.667137706713616*^9, 3.667137722485518*^9}, {
  3.667139301762236*^9, 3.6671393069977317`*^9}, {3.667140163891056*^9, 
  3.6671401847009478`*^9}}],

Cell[BoxData[
 Graphics3DBox[{GraphicsComplex3DBox[CompressedData["
1:eJxlmnlU1dUWxy/IqIIXuMwCF+hpmhJaob7QezOWmRW6DBPLckokehrlxNKe
[encoded data, 5160 characters]
+EP+hDNngDOXID5w5gbYob7IeVd+Sn5WnPkDnHkC+v8D8cNuTg==
    "], {{
      {RGBColor[0.880722, 0.611041, 0.142051], EdgeForm[None], Specularity[
        GrayLevel[1], 3], 
       StyleBox[GraphicsGroup3DBox[{Polygon3DBox[CompressedData["
1:eJwt1FlIVUEcx/E5xxYKtFIjU6NMUrlpG+2kRRGUmNHyEmTKrYQo7jVpz9Iy
eimpKC0qNMrlIaKCFnooKrWQAjWLiCBpofWlxNSw7TvMD+6HOf/ZztyZ/5yk
YHhlyDfGbEQEEpCIeIz1jBmBSMQjAaMRhVjVj2JwNGIxlzgTcxBg/GRMwmPi
52hFPRpRB34mBpGIY3whFUEkIg4jUUBbEIt4bkO75qmibhM2YDMqEUIKUjEB
d3AB1WhADo7iNeNfoAOrsAapvD+Ccgx8LEMucnCaMadwHF/xDV8wnjG9tPch
jCKEEI1hWn8v/frQgxbiZ/iE4cRR2h+7ER7+8VhCeRh7kUE8zp4DmtBs3Nq+
U/7QGrrQrfnzcRJ5+Em/gaxvADp5/oA3+E1bv3Hvmkk8H7NwgrhI//Ez8Uet
cxDxdK0hQJyu832Pd5qzAOU4iDLs0/qnMCZNZ3GAOAvzsB5bdNYPaWvEAywh
ztae52Md1mIhZmudi9HjuXwoYcxb7Ect6nEVf2kr1Xq2EoeVG8uRa9+D+7Q1
owmriVco59vQiic2V2irxhE8JW5XfRlK9d4ztFWoz27iPdiFoez7ds/diyrK
blTaXKNtJ3ZgMPEQ5eE5nMdZ3LQ5p/61qFF9CnMlYyKSGJ+ss76MK7iNdNoy
1OcW8UXVF9t89F1+ziCehkxkYYGei7HNuDOqoOzUfTmEcv2vGtzQnVqKbO2n
/X4U6j6+xCt7z3AN13Uu/cz7x3M5mYaA7+5dF3W/dI/yEOO7c5+KBn0r7uIe
HuESjunsWpi3Q/nzH1I3kdg=
           "]], Polygon3DBox[CompressedData["
1:eJxNl3mYTlUcx+99mcGYylKWDAZjmEmUKKVEIUuiYUoIk5SSZCntu2yhUCjK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           "]], Polygon3DBox[CompressedData["
1:eJwt1XdsTlEYx/Hzvjap2mqUUoqqvUcRIlZtEmLXCEGNIPYmEmqv2IpasWIH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           "]]}],
        Lighting->{{"Ambient", 
           RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, {
          "Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{0, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}}, 
     {GrayLevel[0], Line3DBox[CompressedData["
1:eJwt0M0rwwEYB/DffpNcWHndEnHGSTntohV3f8HSYi4kNU3yVshtO4rdkUzc
tnKglhQnakJt/CM+i8Onvn0Pz/P0jM6vzC1HgiBIE9JGN30MMcwIE0wyRZIZ
ZpkmxTY73HLDNz88UeORB+5545UGLzzzwTv11k4HDdBPgkG++KRJgy7HxliS
syySYYG4PsGqvEaH3E5e3uCATbaI6EOi4d8DLnUXnHJCiWMKHHJEkWuuKHPG
OTXuqFBl38hdcqyzxxjjxOikh97/3/8C/qMsgQ==
       "]]}},
    VertexNormals->CompressedData["
1:eJztmksKwjAQhmvbteDOrQdw6wW8gHgEwbV3qB7IG1TwIoIIHsOCuikMk6TJ
PJLZKH5IHv/8k0zSrg6n/bGuqmo9fDTDdzN/7Da3e98tlq/t9d1/fz97iNc/
fkZ4i3DffjE+Hk/s/3fCxm+clofGHfL/DGgf4lJ0+PM2c9/mOi/jOvJLKx/r
CeWR5ZcMXrr/MR9idSxVfculg6s+odzWActHCT63OpBGT+Npeeh+VEocsfN4
ah2guJSif6k8dN/JrR6w86CO+eZyrjEddPhNS7xit88Vl9L6LY3nrvM47y5K
1mftcYk1fu06aJmva7+tZ/vS6iJsPFL95ns/U0+MO7cO3D6JnUdU90VSdDCe
R1y0j18Kh96HjKXz1Pt81/2Ca52U5kNXnaF6ybcOkVZHGaf17dR2qJ5bSasD
tTzHT70ehr6fI80P1Ppzn19StRN7f6G6P/e9fzDOm0cfeOmLxg==
     "]], GraphicsComplex3DBox[CompressedData["
1:eJx1mX1o1WUUx+9255TpxsplztjcMgQhwhLBIrw36g97k4ggs1CzNJGkhWKi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    "], {{
      {RGBColor[0.880722, 0.611041, 0.142051], EdgeForm[None], Specularity[
        GrayLevel[1], 3], 
       StyleBox[GraphicsGroup3DBox[Polygon3DBox[CompressedData["
1:eJxNmHecz3Ucx79f++yOs8fd2XHuuDPDkXEdznayM8444844hfYgFQ2FJpV2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          "]]],
        Lighting->{{"Ambient", 
           RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, {
          "Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{0, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}}, 
     {GrayLevel[0], 
      Line3DBox[{24, 25, 165, 280, 271, 272, 281, 234, 211, 212, 230, 226, 
       227, 228, 232, 233, 236, 252, 254, 258, 259, 323, 320, 321, 311, 312, 
       337, 338, 340, 339, 315, 316, 334, 343, 371, 366, 364, 374, 157, 156, 
       161, 124, 126, 119, 118, 170, 173, 200, 198, 197, 180, 179, 183, 182, 
       188, 58, 57, 59, 108, 107, 81, 80, 90, 89, 93, 92, 94, 95, 96, 331, 
       105, 102, 103, 31, 24}]}},
    VertexNormals->CompressedData["
1:eJztyLENQFAUQNGHXvMnMIieVquT6IjOKDqz/CXMYQYKS0jObW5ymmkb5jIi
9iKien+sSzrHO9d9N6X2yvHFOeecc84555xzzjnnnHPOOeecc875H/0BJ1tM
zg==
     "]], GraphicsComplex3DBox[CompressedData["
1:eJxlmmlY1dUWxg/zIOcww2GSA6gpjtdZwziiOVXEVQwew9QcItSuqRFXLbDB
[encoded data, 5280 characters]

    "], {{
      {RGBColor[0.880722, 0.611041, 0.142051], EdgeForm[None], Specularity[
        GrayLevel[1], 3], 
       StyleBox[GraphicsGroup3DBox[{Polygon3DBox[CompressedData["
1:eJwt0U8ow2Ecx/GHScJFaaymOKBcRomDslI7jUQcMGQO2hYupDnIhcPMYTlJ
2lbKn1zIn5SDnZS05aTIhRWShHCT9y+fw6vn+Tzfb8/v9/v+qvyT3RO5xpgm
2OBGG1oxh1mE0Qmv9lvYwRfKcowphx0P5HzWe9YSVofOK8iVcOIMKdxad1Db
xiamsIAwSqnZ1R8jr6ongiiWcETtGIfYJx9gDzXkWlTjGz96z3pqDXAhiw31
+6lFMAIP+QoZtJCbNYcLclrnBZoTW2PN7UX7d7zhA40cvOpZ13jCI+6o3ejb
6+BCP9qpdcGLZ3LW/M+wCMUotGZBrUM9a+R1xPGJXz03hhUkrDnTl8Ipzsm7
6s8jL7JGEWQf0sxnyNOa2wDZh0HMI6B9klpa9/eQezGEZXJGd/rQp+8apnai
nnFyCAEkyXG9W5B8qfMxjOpf/AFJSVId
           "]], Polygon3DBox[CompressedData["
1:eJxNmHd0l0UWhr9BmouAUlbEVSEgJSCKFKWDoFFWFIO0BREVIiJVbIfQm2LB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           "]], Polygon3DBox[CompressedData["
1:eJwt1Ftoj2EcB/C/GYlckBxnSAhpEyPk3JJYoonNzAxpE6KhKXIec4hcMNIM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           "]]}],
        Lighting->{{"Ambient", 
           RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, {
          "Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{0, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}}, 
     {GrayLevel[0], Line3DBox[CompressedData["
1:eJwt0L1KggEAheEvgiJpUJqiyQsQREIabAjCsLG1oVKixR8U1JYK2qJcpCms
pbkxhGoKG6KlpDFBcqgphW6gR2h4tjO8nGi2tFGcCIJgk2mmmGGRBEmWSLHC
KmnyFOnwzAtXtLjhmgvOafLGK12euOeWNg8EIibp8MglLX754psfhnzwTpce
I1IsM+CTPutkSLPGHQVKHHDIETvk2GWPBnX2qVKjTIVjTjnjZLyRXmOLbeLE
WCDELBHCzDH///Mf7AMuTg==
       "]]}},
    VertexNormals->CompressedData["
1:eJztWrsNwkAMPaAGCipKGhRIDYOwABISBRUlAzABe9BToWyQHWihQWIBKKA8
EaPn+PlIFekpOvnz/Hx2MlptF+t2COHRCqHzek5259vgcCp649lmvr8Wy2F5
L4+XIoZP/wzPhLiVPWxxi+FeeCW1M1W/2PiZv/E+STwbPG3cS11bxSGGs/XN
Bk8Dj/EHVadNvaehq1Z5ZPNL+n4z19jGLSfjMyo+Mb9Q79flb5fEHlR9WdUd
iudsPPGCo/KO0kkre9D3Rq/6YOUvW1/zjmegvGjXo/e8p7ofZosnij9W+izd
V1jVC+p8qW5o73NYca3vF6nHjV2XrM5h449Ub7V1z3tdeOl33nmbOl6173jn
GxtPtHXeC/9R86l2n/rWj1jma+s8suhDXf1Fy/5f+VDVntj50v35v+2FUPdY
K3342KM9b9YdH7b7RqyOUPsN1P9XUvu96OoTYVMpzw==
     "]], 
   {RGBColor[1, 0, 0], PointSize[0.05], Point3DBox[{1, -3, 4.5}]}},
  Axes->True,
  AxesLabel->{
    FormBox["x", TraditionalForm], 
    FormBox["y", TraditionalForm], 
    FormBox["z", TraditionalForm]},
  BoxRatios->{1, 1, 1},
  DisplayFunction->Identity,
  FaceGridsStyle->Automatic,
  Method->{"DefaultBoundaryStyle" -> Directive[
      GrayLevel[0.3]]},
  PlotRange->{{-10, 10}, {-10, 10}, {-10, 10}},
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02], 
    Scaled[0.02]},
  Ticks->{Automatic, Automatic, Automatic}]], "Output",
 CellChangeTimes->{
  3.667222073829743*^9},ImageCache->GraphicsData["CompressedBitmap", "\<\
[encoded data, 14160 characters]
icKmjQ==\
\>"]]
}, {2}]],

Cell["\<\
H\[AAcute]rom \[AAcute]ltal\[AAcute]nos helyzet\[UDoubleAcute] s\[IAcute]kot \
kaptunk. L\[AAcute]that\[OAcute], hogy a h\[AAcute]rom s\[IAcute]k egy \
pontban metszi egym\[AAcute]st, \[IAcute]gy egy megold\[AAcute]sa van az \
egyenletrendszernek.\
\>", "Text",
 CellChangeTimes->{{3.6672231232667675`*^9, 3.6672231803812923`*^9}},
 TextJustification->1.]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
2. eset: A f\[UDoubleDot]ggetlen egyenletek sz\[AAcute]ma 1-gyel kisebb, mint \
a v\[AAcute]ltoz\[OAcute]k sz\[AAcute]ma: 2 f\[UDoubleDot]ggetlen egyenlet, 3 \
v\[AAcute]ltoz\[OAcute]\
\>", "Subsubsection",
 CellChangeTimes->{3.6672221844100676`*^9}],

Cell[CellGroupData[{

Cell[TextData[{
 "\t1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+5\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+3\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=28\n\t3\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+0\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0\n\t6\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+2\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+0\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0"
}], "Text",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.66722221138461*^9, 3.667222212910698*^9}, 
   3.6672222598823843`*^9}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"n21", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "5", ",", "3"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sik21", "=", 
   RowBox[{"n21", ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], ")"}]}]}], ";"}]}], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6671366808089375`*^9, 3.667136682584039*^9}, {
   3.6671392786087813`*^9, 3.6671392811124535`*^9}, {3.6671393899621124`*^9, 
   3.6671393950955343`*^9}, 3.6671394575352163`*^9, {3.66722223865217*^9, 
   3.6672222598833847`*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"n22", "=", 
   RowBox[{"{", 
    RowBox[{"3", ",", "1", ",", "0"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sik22", "=", 
   RowBox[{"n22", ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], ")"}]}]}], ";"}]}], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6671366843091373`*^9, 3.6671367006360717`*^9}, {
  3.6671392832288656`*^9, 3.667139288901652*^9}, {3.667139397082861*^9, 
  3.6671394013807335`*^9}, {3.6672222413993273`*^9, 3.6672222598833847`*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"n23", "=", 
   RowBox[{"{", 
    RowBox[{"6", ",", "2", ",", "0"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sik23", "=", 
   RowBox[{"n23", ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], ")"}]}]}], ";"}]}], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6671367147988815`*^9, 3.6671367197911673`*^9}, {
  3.667139290518731*^9, 3.66713929274922*^9}, {3.667139403065855*^9, 
  3.667139406822362*^9}, {3.667139464319743*^9, 3.6671394696563053`*^9}, {
  3.6672222438654685`*^9, 3.6672222598833847`*^9}}]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"ContourPlot3D", "[", 
    RowBox[{
     RowBox[{"sik21", "\[Equal]", "28"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"Mesh", "\[Rule]", "None"}]}], "]"}], ",", " ", 
   RowBox[{"ContourPlot3D", "[", 
    RowBox[{
     RowBox[{"sik22", "\[Equal]", "0"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"Mesh", "\[Rule]", "None"}]}], "]"}], ",", " ", 
   RowBox[{"ContourPlot3D", "[", 
    RowBox[{
     RowBox[{"sik23", "\[Equal]", "0"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"Mesh", "\[Rule]", "None"}]}], "]"}], ",", " ", 
   RowBox[{"AxesLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"x", ",", "y", ",", "z"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.667136754439149*^9, 3.6671367752563396`*^9}, {
  3.6671373840481606`*^9, 3.667137405438384*^9}, {3.6671376447290707`*^9, 
  3.667137674998802*^9}, {3.667137706713616*^9, 3.667137722485518*^9}, {
  3.667139301762236*^9, 3.6671393069977317`*^9}, {3.667139411052188*^9, 
  3.667139418416105*^9}, {3.667139483085271*^9, 3.6671395043924894`*^9}}],

Cell[BoxData[
 Graphics3DBox[{GraphicsComplex3DBox[CompressedData["
1:eJxlmWlQlFcWhptmR1bZUbDpJnEZY0ypcbe/KJMijgsBo4gLKoKIEnGLxBjt
[encoded data, 4200 characters]
7DOP+j8mcfqj
    "], {{
      {RGBColor[0.880722, 0.611041, 0.142051], EdgeForm[None], Specularity[
        GrayLevel[1], 3], 
       StyleBox[GraphicsGroup3DBox[{Polygon3DBox[CompressedData["
1:eJwt01toj2EYAPBvmGGxRA4lpYaaXTCMIUxcyGphI+Y4mvMcp4jIuSzCzCkM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           "]], Polygon3DBox[CompressedData["
1:eJw1lnmUSFUcx++rES0Y6zTGNkbWmEJG2RtbtiwdSymZkCJLNAxjS0LWjGTL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           "]], Polygon3DBox[CompressedData["
1:eJwt1WdMFkEQgOE9UVBQiB2BaLBgA2NBmohiiR0sWMACYsEKCFgRERArYgEr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           "]]}],
        Lighting->{{"Ambient", 
           RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, {
          "Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{0, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}}, 
     {GrayLevel[0], Line3DBox[CompressedData["
1:eJwt0L1KggEYBeCvVukGHCxbk3TQKSQJjLIhFU1RvwYlIn8Xb6KxqMlmI3IO
IQu8iwi6iOgGfISGBw68cOC88faoPNwIgqDCJuscUqLIgCoX3Dj26XJNmRLn
FLkkpEWOQxo0mTLjmRde+dX5R0ZOs8sOSVLskyDGNnvcMqZKjTpPTHjkgTvu
6enuM+KKDt31Dt6Y88GCdz5ZkiLCFkl++OaLPEcckOWYE84ocEr0/5crZ78j
jg==
       "]]}},
    VertexNormals->CompressedData["
1:eJxTTMoPSmViYGDYzsjAwAykpa5l9pxddHT/Qu+W9w3cr/dPSfDXlLJ6sH9U
fHiLS0PFF6CJywyQvYMtfHCJS9LY/TJDPHxGmvhQT8+j4sTlR2LFh0r6oVb5
T2v3D1T40LqcHxUfFR9O+WVUfLTcGA23UfFR8ZEpPpp/R8NtVHxUnFbtz8mD
1L+k9pepld+pFc6E3AMTnzrA6WeolZPEhhsuf+EKB1LFSc1fA5U+h1r8jobD
qPhgTD+DrZ4ltXwbbPlOkkr+Gh2XG1n5iNriA5WPqN2epJX51LKXVHMGW3t+
qOeXwRYOw1Wc1HQ7VOKF1P4jufmX3v3iUfGBTZ8ADbfzlA==
     "]], GraphicsComplex3DBox[CompressedData["
1:eJx1mX1o1WUUx+9255TpxsplztjcMgQhwhLBIrw36g97k4ggs1CzNJGkhWKi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    "], {{
      {RGBColor[0.880722, 0.611041, 0.142051], EdgeForm[None], Specularity[
        GrayLevel[1], 3], 
       StyleBox[GraphicsGroup3DBox[Polygon3DBox[CompressedData["
1:eJxNmHecz3Ucx79f++yOs8fd2XHuuDPDkXEdznayM8444844hfYgFQ2FJpV2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          "]]],
        Lighting->{{"Ambient", 
           RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, {
          "Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{0, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}}, 
     {GrayLevel[0], 
      Line3DBox[{24, 25, 165, 280, 271, 272, 281, 234, 211, 212, 230, 226, 
       227, 228, 232, 233, 236, 252, 254, 258, 259, 323, 320, 321, 311, 312, 
       337, 338, 340, 339, 315, 316, 334, 343, 371, 366, 364, 374, 157, 156, 
       161, 124, 126, 119, 118, 170, 173, 200, 198, 197, 180, 179, 183, 182, 
       188, 58, 57, 59, 108, 107, 81, 80, 90, 89, 93, 92, 94, 95, 96, 331, 
       105, 102, 103, 31, 24}]}},
    VertexNormals->CompressedData["
1:eJztyLENQFAUQNGHXvMnMIieVquT6IjOKDqz/CXMYQYKS0jObW5ymmkb5jIi
9iKien+sSzrHO9d9N6X2yvHFOeecc84555xzzjnnnHPOOeecc875H/0BJ1tM
zg==
     "]], GraphicsComplex3DBox[CompressedData["
1:eJx1mX1o1WUUx+9255TpxsplztjcMgQhwhLBIrw36g97k4ggs1CzNJGkhWKi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    "], {{
      {RGBColor[0.880722, 0.611041, 0.142051], EdgeForm[None], Specularity[
        GrayLevel[1], 3], 
       StyleBox[GraphicsGroup3DBox[Polygon3DBox[CompressedData["
1:eJxNmHecz3Ucx79f++yOs8fd2XHuuDPDkXEdznayM8444844hfYgFQ2FJpV2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          "]]],
        Lighting->{{"Ambient", 
           RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, {
          "Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{0, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}}, 
     {GrayLevel[0], 
      Line3DBox[{24, 25, 165, 280, 271, 272, 281, 234, 211, 212, 230, 226, 
       227, 228, 232, 233, 236, 252, 254, 258, 259, 323, 320, 321, 311, 312, 
       337, 338, 340, 339, 315, 316, 334, 343, 371, 366, 364, 374, 157, 156, 
       161, 124, 126, 119, 118, 170, 173, 200, 198, 197, 180, 179, 183, 182, 
       188, 58, 57, 59, 108, 107, 81, 80, 90, 89, 93, 92, 94, 95, 96, 331, 
       105, 102, 103, 31, 24}]}},
    VertexNormals->CompressedData["
1:eJztyLENQFAUQNGHXvMnMIieVquT6IjOKDqz/CXMYQYKS0jObW5ymmkb5jIi
9iKien+sSzrHO9d9N6X2yvHFOeecc84555xzzjnnnHPOOeecc875H/0BJ1tM
zg==
     "]]},
  Axes->True,
  AxesLabel->{
    FormBox["x", TraditionalForm], 
    FormBox["y", TraditionalForm], 
    FormBox["z", TraditionalForm]},
  BoxRatios->{1, 1, 1},
  DisplayFunction->Identity,
  FaceGridsStyle->Automatic,
  ImageSize->{371.4700512768338, 395.2127040271741},
  ImageSizeRaw->Automatic,
  Method->{"DefaultBoundaryStyle" -> Directive[
      GrayLevel[0.3]]},
  PlotRange->{{-10, 10}, {-10, 10}, {-10, 10}},
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02], 
    Scaled[0.02]},
  Ticks->{Automatic, Automatic, Automatic},
  ViewPoint->{0.9528936012600234, -2.697639917230093, 1.8068571226426624`},
  ViewVertical->{-0.178701292879906, -0.15357922625462256`, 
   0.9718432328241431}]], "Output",
 CellChangeTimes->{3.6672222479597025`*^9}]
}, {2}]],

Cell["\<\
Ebben az esetben k\[EAcute]t s\[IAcute]k egybeesik, l\[AAcute]that\[OAcute], \
hogy a h\[AAcute]rom s\[IAcute]k \[IAcute]gy egy egyenesben metszi egym\
\[AAcute]st. Teh\[AAcute]t az egyenletrendszernek v\[EAcute]gtelen sok megold\
\[AAcute]sa van, m\[EAcute]gpedig \[UAcute]gy, hogy egy szabad v\[AAcute]ltoz\
\[OAcute]ja lesz a megold\[AAcute]soknak.\
\>", "Text",
 CellChangeTimes->{{3.6672232063154883`*^9, 3.6672232838867607`*^9}},
 TextJustification->1.]
}, Open  ]],

Cell[CellGroupData[{

Cell["\<\
3. eset: A f\[UDoubleDot]ggetlen egyenletek sz\[AAcute]ma 2-vel kisebb, mint \
a v\[AAcute]ltoz\[OAcute]k sz\[AAcute]ma: 1 f\[UDoubleDot]ggetlen egyenlet, 3 \
v\[AAcute]ltoz\[OAcute]\
\>", "Subsubsection",
 CellChangeTimes->{3.667222281796638*^9}],

Cell[CellGroupData[{

Cell[TextData[{
 "\t1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+5\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+2\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=4\n\t3\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+15\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+6\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=12\n\t6\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+30\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+12\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=24"
}], "Text",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6672223055719976`*^9, 3.667222307144088*^9}, 
   3.667222344450221*^9}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"n31", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "5", ",", "2"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sik31", "=", 
   RowBox[{"n31", ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], ")"}]}]}], ";"}]}], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6671366808089375`*^9, 3.667136682584039*^9}, {
   3.6671392786087813`*^9, 3.6671392811124535`*^9}, {3.6671393899621124`*^9, 
   3.6671393950955343`*^9}, 3.6671394575352163`*^9, {3.6671395784158983`*^9, 
   3.667139596513982*^9}, {3.667222321643917*^9, 3.667222344450221*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"n32", "=", 
   RowBox[{"{", 
    RowBox[{"3", ",", "15", ",", "6"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sik32", "=", 
   RowBox[{"n32", ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], ")"}]}]}], ";"}]}], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6671366843091373`*^9, 3.6671367006360717`*^9}, {
  3.6671392832288656`*^9, 3.667139288901652*^9}, {3.667139397082861*^9, 
  3.6671394013807335`*^9}, {3.6671395833752117`*^9, 3.667139605564023*^9}, {
  3.667222324685091*^9, 3.6672223444512215`*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"n33", "=", 
   RowBox[{"{", 
    RowBox[{"6", ",", "30", ",", "12"}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sik33", "=", 
   RowBox[{"n33", ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], ")"}]}]}], ";"}]}], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6671367147988815`*^9, 3.6671367197911673`*^9}, {
  3.667139290518731*^9, 3.66713929274922*^9}, {3.667139403065855*^9, 
  3.667139406822362*^9}, {3.667139464319743*^9, 3.6671394696563053`*^9}, {
  3.66713958895093*^9, 3.6671396137044563`*^9}, {3.667222327180234*^9, 
  3.6672223444512215`*^9}}]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"ContourPlot3D", "[", 
    RowBox[{
     RowBox[{"sik31", "\[Equal]", "4"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"Mesh", "\[Rule]", "None"}]}], "]"}], ",", " ", 
   RowBox[{"ContourPlot3D", "[", 
    RowBox[{
     RowBox[{"sik32", "\[Equal]", "12"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"Mesh", "\[Rule]", "None"}]}], "]"}], ",", " ", 
   RowBox[{"ContourPlot3D", "[", 
    RowBox[{
     RowBox[{"sik33", "\[Equal]", "24"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"Mesh", "\[Rule]", "None"}]}], "]"}], ",", " ", 
   RowBox[{"AxesLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"x", ",", "y", ",", "z"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.667136754439149*^9, 3.6671367752563396`*^9}, {
  3.6671373840481606`*^9, 3.667137405438384*^9}, {3.6671376447290707`*^9, 
  3.667137674998802*^9}, {3.667137706713616*^9, 3.667137722485518*^9}, {
  3.667139301762236*^9, 3.6671393069977317`*^9}, {3.667139411052188*^9, 
  3.667139418416105*^9}, {3.667139483085271*^9, 3.6671395043924894`*^9}, {
  3.6671396217678375`*^9, 3.667139640448305*^9}}],

Cell[BoxData[
 Graphics3DBox[{GraphicsComplex3DBox[CompressedData["
1:eJxl2n+Uz3UWx/ExzCBmjDHKjPystKk0aSsOuzNnczqpTR0/dtVKyqZWkQrZ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    "], {{
      {RGBColor[0.880722, 0.611041, 0.142051], EdgeForm[None], Specularity[
        GrayLevel[1], 3], 
       StyleBox[GraphicsGroup3DBox[{Polygon3DBox[CompressedData["
1:eJw11GtMT3Ecx/Hzl1wiobBESbaarOhmI4u1GdWa0kY36aIQ/mXCTIslbKXE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           "]], Polygon3DBox[CompressedData["
1:eJwt1ndsVlUYx/F7K0pAAUHZEoaVJWBLmBUoG4QyZIlFRIlCIVBGbQtS2QFK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           "]], Polygon3DBox[CompressedData["
1:eJwt1WUUVEUUAOBdBKVUGhGQkAaVBpFQQRokREIQJATpVpCUUDoUBGlBSrqk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           "]]}],
        Lighting->{{"Ambient", 
           RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, {
          "Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{0, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}}, 
     {GrayLevel[0], Line3DBox[CompressedData["
1:eJwt0LFKQgEUBuDrkDo1R1RgkQ2Vc+ESougWBBkRhF3F8bpKtSSIERSkQtEY
CEE4N/kMLtZkL5INfULDN/xwzvnhpMLGURQLguCYJAnyLLNEgYgqIUNe6NGn
Q5tHRjzzxIA33hkz4ZvpfF5hhwfu+WCHbTKk2WSNVbbYZZFf+z/MWJDjJLji
lju69OjzyjllTqhwyhlFShxSp8YFITfut7jmkiZF9tjnixQbrPNJjgOyrPz/
8w/dPCVS
       "]]}},
    VertexNormals->CompressedData["
1:eJztWbENwjAQNLAELUvQ0SJqBqBAomacYNEwAhPgCjECDSuwA0jUVvj47L9X
vopysqzL/f194iz2x+1hGkK4T0KYfa+n62Xd7R7p9trMV8t3+t0/k+OOO+54
LTyS8XHccccdb4V3ZHw8/x0v8a0UR/GJhesjKU8UflZ63tr6s+2j5Yccf1Rf
a/mWDdfyCaqOVvRky8/WOrP6KjdH2Hyl5c+x5XZt/mx+kPZvTn9pXVD6/OsT
K33N6jf2nETxkc7r3Pq+eYeqV46P1P9a37konUv3R69vrRtaH628tZLnbHzY
5oXzx+YzG26V/9A5ODRXU2Of1DrP6Xv/t96n1nGr/Yju67HroO232v0uPRdC
/TdB8Zd+R1s5n2fxIbqO0nn3AbDr3rw=
     "]], GraphicsComplex3DBox[CompressedData["
1:eJxl2n+Uz3UWx/ExzCBmjDHKjPystKk0aSsOuzNnczqpTR0/dtVKyqZWkQrZ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    "], {{
      {RGBColor[0.880722, 0.611041, 0.142051], EdgeForm[None], Specularity[
        GrayLevel[1], 3], 
       StyleBox[GraphicsGroup3DBox[{Polygon3DBox[CompressedData["
1:eJw11GtMT3Ecx/Hzl1wiobBESbaarOhmI4u1GdWa0kY36aIQ/mXCTIslbKXE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           "]], Polygon3DBox[CompressedData["
1:eJwt1ndsVlUYx/F7K0pAAUHZEoaVJWBLmBUoG4QyZIlFRIlCIVBGbQtS2QFK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           "]], Polygon3DBox[CompressedData["
1:eJwt1WUUVEUUAOBdBKVUGhGQkAaVBpFQQRokREIQJATpVpCUUDoUBGlBSrqk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           "]]}],
        Lighting->{{"Ambient", 
           RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, {
          "Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{0, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}}, 
     {GrayLevel[0], Line3DBox[CompressedData["
1:eJwt0LFKQgEUBuDrkDo1R1RgkQ2Vc+ESougWBBkRhF3F8bpKtSSIERSkQtEY
CEE4N/kMLtZkL5INfULDN/xwzvnhpMLGURQLguCYJAnyLLNEgYgqIUNe6NGn
Q5tHRjzzxIA33hkz4ZvpfF5hhwfu+WCHbTKk2WSNVbbYZZFf+z/MWJDjJLji
lju69OjzyjllTqhwyhlFShxSp8YFITfut7jmkiZF9tjnixQbrPNJjgOyrPz/
8w/dPCVS
       "]]}},
    VertexNormals->CompressedData["
1:eJztWbsNAjEMDbAELUvQ0SJqBqBAomac4zpGYAJSIUagYQV2AAnRIEU5O/6C
q9M9nSJ/np8d32y7X+/GKaXLKKXJ63k4HZfd5prP99V0MX/k9/stB47DO6bv
e6N+Qf39VZwqDr0TOwP3xavAYbi23tbsycFDVpxbh/8Fp6qjzzle80IdBy37
SzpQyou1fHHPaSUcGjcv8zbUTigfvPBKi4fWztE6X9pOrA5r5Usq/kPn0lZ9
gMafen6m0h8vdYGNs3T/9dLvqPq7Fx5C4yB9Ppa32vVLvQewtvfA8pxq/uTK
LzbO3HUknUerfGuNp5RfrbokZSfXXOeN/0P9Le27WvNV6xfUfCjZb42f3Hou
7a/UHB544Bb6r5c+yF3XXLqtlV/qOZlbD63eE7HzgHZde8epdExrz2Ntb0P1
P8ja/a5m/3edUumM1j72CWIe3oA=
     "]], GraphicsComplex3DBox[CompressedData["
1:eJxl2n+Uz3UWx/ExzCBmjDHKjPystKk0aSsOuzNnczqpTR0/dtVKyqZWkQrZ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    "], {{
      {RGBColor[0.880722, 0.611041, 0.142051], EdgeForm[None], Specularity[
        GrayLevel[1], 3], 
       StyleBox[GraphicsGroup3DBox[{Polygon3DBox[CompressedData["
1:eJw11GtMT3Ecx/Hzl1wiobBESbaarOhmI4u1GdWa0kY36aIQ/mXCTIslbKXE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           "]], Polygon3DBox[CompressedData["
1:eJwt1ndsVlUYx/F7K0pAAUHZEoaVJWBLmBUoG4QyZIlFRIlCIVBGbQtS2QFK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           "]], Polygon3DBox[CompressedData["
1:eJwt1WUUVEUUAOBdBKVUGhGQkAaVBpFQQRokREIQJATpVpCUUDoUBGlBSrqk
G7u7jt3deYxvz7s/vrOzb+6buVNvSvUe1mFollQq1Z9s7KUbg9jDfmZwLzOZ
zjSWsJj5LGQjz/Miz/IyL3Efs1jFgojfTm9uYyfbmM1c5rA83tlBT27lOIdZ
y8N8wud8yBqO8hhHWM0mVnCGryKvL/iM7/ieb3kkct/KFjYzL3Laza7IaWW0
e5qT0e4p3ucb3uMJPuCjyOvLqD/Gopi3pSxjPQPowYYYU1Yya5GOtTiPF3gu
5vIVXqWKgIqUpAyVKUEpylOcYhygKAWoFO+U4/Kov4yyVKUav2j7J65SrktN
alAn6kuTm1xUiP62sZWDXMol7GAn+1nIHDazi308ykbe1dc7mTVQnskMvo51
OaZ8guO87f+nqaR8Mto5xBmupl70v5cjnOYcu6lFbbKkk4nNjGcLmyKH7ZHr
UQ6zjtXRznzmRv4LmEcRqqeTOfpNk3/wM/9wvmfZ+FN5MlMz+9z/HGSnFW1p
Q2tacJOYDgxVvt1vP65Tbk4zGnMNXehGV3rRmfbcQBN60j3THg3oREc6MJxh
9KFpvNOfflzPtVGXj/z0zeQS9b/K58dUMqa/+YsL08m4f+fi2A+FYu0LUzCd
7Lmx6sekkrHnJC8NqR9jahS5/ivmv8x+V86aTubyjojPw2AGMZABUR4Sc/mU
2BNx9p7mSSZ5PoFFLGY2aUYyixHppK9CYguQn8IUpAjFM+OiaNRlpxi5yJFZ
Zy6K85mbvOQhZ2btaEH1OMfNacooSnBZZv4oH+WSlKUSlaOdfFxBEy6I/hpH
XlW5khrUirZfozSleJ2GvMkbnOXxOGfPxPy8xbmoG8ndTGE4w6hHI+pTLcZU
jgpRP4LR1KYuzagZOTWI/utkviPRxp0mYhwPcH+sy7jMc8YzIXK4ma50pi3t
WCa2ZZyVB1nCKpazgalxvsfTI/b7+uhvRcRPZ0rEj+Ue7mIioxnFmChPjn2y
lHZxpqbFOwcy+zLOaOa+XOvZmnTyu5KH0sn341AquavWcTCV3Et9GMpghqSS
u69KrHMnbkkld0GX2A9laBVz0YaWtKdjKvledI/5uZGBqeS+bh3rMomJEf9x
KrnD9/FDKrn7eqWSvV6Rvqnkfj0l7z3p5Jt5Np18W/8HvATroA==
           "]]}],
        Lighting->{{"Ambient", 
           RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, {
          "Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{0, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}}, 
     {GrayLevel[0], Line3DBox[CompressedData["
1:eJwt0LFKQgEUBuDrkDo1R1RgkQ2Vc+ESougWBBkRhF3F8bpKtSSIERSkQtEY
CEE4N/kMLtZkL5INfULDN/xwzvnhpMLGURQLguCYJAnyLLNEgYgqIUNe6NGn
Q5tHRjzzxIA33hkz4ZvpfF5hhwfu+WCHbTKk2WSNVbbYZZFf+z/MWJDjJLji
lju69OjzyjllTqhwyhlFShxSp8YFITfut7jmkiZF9tjnixQbrPNJjgOyrPz/
8w/dPCVS
       "]]}},
    VertexNormals->CompressedData["
1:eJztWbsNAjEMDbAELUvQ0SJqBqBAomac4zpGYAJSIUagYQV2AAnRIEU5O/6C
q9M9nSJ/np8d32y7X+/GKaXLKKXJ63k4HZfd5prP99V0MX/k9/stB47DO6bv
e6N+Qf39VZwqDr0TOwP3xavAYbi23tbsycFDVpxbh/8Fp6qjzzle80IdBy37
SzpQyou1fHHPaSUcGjcv8zbUTigfvPBKi4fWztE6X9pOrA5r5Usq/kPn0lZ9
gMafen6m0h8vdYGNs3T/9dLvqPq7Fx5C4yB9Ppa32vVLvQewtvfA8pxq/uTK
LzbO3HUknUerfGuNp5RfrbokZSfXXOeN/0P9Le27WvNV6xfUfCjZb42f3Hou
7a/UHB544Bb6r5c+yF3XXLqtlV/qOZlbD63eE7HzgHZde8epdExrz2Ntb0P1
P8ja/a5m/3edUumM1j72CWIe3oA=
     "]]},
  Axes->True,
  AxesLabel->{
    FormBox["x", TraditionalForm], 
    FormBox["y", TraditionalForm], 
    FormBox["z", TraditionalForm]},
  BoxRatios->{1, 1, 1},
  DisplayFunction->Identity,
  FaceGridsStyle->Automatic,
  Method->{"DefaultBoundaryStyle" -> Directive[
      GrayLevel[0.3]]},
  PlotRange->{{-10, 10}, {-10, 10}, {-10, 10}},
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02], 
    Scaled[0.02]},
  Ticks->{Automatic, Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.6672223300513983`*^9}]
}, {2}]],

Cell["\<\
Mind a h\[AAcute]rom s\[IAcute]k egybeesik, \[IAcute]gy teh\[AAcute]t a s\
\[IAcute]kok metszete egy s\[IAcute]k, azaz v\[EAcute]gtelen sok megold\
\[AAcute]sa van az egyenletrendszernek, \[EAcute]s k\[EAcute]t szabad v\
\[AAcute]ltoz\[OAcute]ja lesz a megold\[AAcute]soknak.\
\>", "Text",
 CellChangeTimes->{{3.667223307362829*^9, 3.667223359604995*^9}},
 TextJustification->1.]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Homog\[EAcute]n line\[AAcute]ris egyenletrendszerek", "Section",
 CellChangeTimes->{3.6672224359784565`*^9}],

Cell[CellGroupData[{

Cell[TextData[StyleBox["Csak a trivi\[AAcute]lis megold\[AAcute]s megold\
\[AAcute]sa az egyenletrendszernek", "Subsection"]], "Subsection",
 CellChangeTimes->{3.667222458467743*^9}],

Cell[CellGroupData[{

Cell[TextData[{
 "\t1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+5\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+4\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0\n\t3\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+0\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0\n\t1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+9\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+6\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0"
}], "Text",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6672224757787333`*^9, 3.6672224769778013`*^9}, 
   3.6672225279927197`*^9}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"n41", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "5", ",", "4"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sik41", "=", 
   RowBox[{"n41", ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], ")"}]}]}], ";"}]}], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6671366808089375`*^9, 3.667136682584039*^9}, {
   3.6671392786087813`*^9, 3.6671392811124535`*^9}, {3.6671393899621124`*^9, 
   3.6671393950955343`*^9}, 3.6671394575352163`*^9, {3.6671395784158983`*^9, 
   3.667139596513982*^9}, {3.6671397689740953`*^9, 3.667139773210923*^9}, 
   3.667139809533167*^9, {3.6672224980160046`*^9, 3.6672225279927197`*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"n42", "=", 
   RowBox[{"{", 
    RowBox[{"3", ",", "1", ",", "0"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sik42", "=", 
   RowBox[{"n42", ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], ")"}]}]}], ";"}]}], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6671366843091373`*^9, 3.6671367006360717`*^9}, {
  3.6671392832288656`*^9, 3.667139288901652*^9}, {3.667139397082861*^9, 
  3.6671394013807335`*^9}, {3.6671395833752117`*^9, 3.667139605564023*^9}, {
  3.6671397758747*^9, 3.667139781140219*^9}, {3.6671398143493805`*^9, 
  3.667139817665599*^9}, {3.6672225004761457`*^9, 3.6672225279937196`*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"n43", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "9", ",", "6"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sik43", "=", 
   RowBox[{"n43", ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], ")"}]}]}], ";"}]}], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6671367147988815`*^9, 3.6671367197911673`*^9}, {
  3.667139290518731*^9, 3.66713929274922*^9}, {3.667139403065855*^9, 
  3.667139406822362*^9}, {3.667139464319743*^9, 3.6671394696563053`*^9}, {
  3.66713958895093*^9, 3.6671396137044563`*^9}, {3.6671398009714537`*^9, 
  3.6671398272860184`*^9}, {3.6672225031292973`*^9, 3.6672225279937196`*^9}}]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"ContourPlot3D", "[", 
    RowBox[{
     RowBox[{"sik41", "\[Equal]", "0"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"Mesh", "\[Rule]", "None"}]}], "]"}], ",", " ", 
   RowBox[{"ContourPlot3D", "[", 
    RowBox[{
     RowBox[{"sik42", "\[Equal]", "0"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"Mesh", "\[Rule]", "None"}]}], "]"}], ",", " ", 
   RowBox[{"ContourPlot3D", "[", 
    RowBox[{
     RowBox[{"sik43", "\[Equal]", "0"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"Mesh", "\[Rule]", "None"}]}], "]"}], ",", " ", 
   RowBox[{"Graphics3D", "[", 
    RowBox[{"{", 
     RowBox[{"Red", ",", 
      RowBox[{"PointSize", "[", "0.05", "]"}], ",", 
      RowBox[{"Point", "[", 
       RowBox[{"{", 
        RowBox[{"0", ",", "0", ",", "0"}], "}"}], "]"}]}], "}"}], "]"}], " ", 
   ",", 
   RowBox[{"AxesLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"x", ",", "y", ",", "z"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.667136754439149*^9, 3.6671367752563396`*^9}, {
  3.6671373840481606`*^9, 3.667137405438384*^9}, {3.6671376447290707`*^9, 
  3.667137674998802*^9}, {3.667137706713616*^9, 3.667137722485518*^9}, {
  3.667139301762236*^9, 3.6671393069977317`*^9}, {3.667139411052188*^9, 
  3.667139418416105*^9}, {3.667139483085271*^9, 3.6671395043924894`*^9}, {
  3.6671396217678375`*^9, 3.667139640448305*^9}, {3.6671398351572695`*^9, 
  3.667139856541547*^9}, {3.667140030598728*^9, 3.6671400432811937`*^9}}],

Cell[BoxData[
 Graphics3DBox[{GraphicsComplex3DBox[CompressedData["
1:eJx1mnlY1WUWxy9c9uV6gcuurDONWwzzjJO4FHecxgzTzEzLlUzELCdcQsYV
[encoded data, 5280 characters]
8Q==
    "], {{
      {RGBColor[0.880722, 0.611041, 0.142051], EdgeForm[None], Specularity[
        GrayLevel[1], 3], 
       StyleBox[GraphicsGroup3DBox[{Polygon3DBox[CompressedData["
1:eJwt031MzVEcx/HfKQuZ0N1lZGITubcskoeNmc3DJpUeNAzjUh6mYlTMyB8Y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           "]], Polygon3DBox[CompressedData["
1:eJxNl3u81/Mdxz+fn1Ihp3Q96ehUp9ONypjSndajWBsyTIYWyjWcR5pSOUWR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           "]], Polygon3DBox[CompressedData["
1:eJwt1WVoV1EYx/F7/7rZMbdZ29RhL3R2Y3c7Y4o5a4qtMzHALnxhYmJggs5O
sAN7BojYgV3o7Po+nN+LD/fc85xz7ukbnTy8w7CA53kDEYTVvuctw0qswSp8
Jj+cZxEUxTfen+IRHuIJHqMesbpohCZojFqojYqogpZq09reiA1Yj6XYpPRB
LMEO2tyEfdiL7biD27iG8ziLGqiGidQZjzK+y7f4OZzBcTQjvykOYDfS1Efr
6y7sVCxN8R0Yg9HYTP23eIl76tMWvMFrxazMLqQhHdfVz+nUn4sZmIf5OEn+
aVzBZVzCLPLnYDZmqvw4pGIPjuKI7+bB5mMPdmMnFpI/GVPVhrV1iPxJGIcX
OOi5b1sftlo72GZrQP5WtZOmMTQkf6y+dwxTcIr8E5pL67uN4T0e4D7eaS6m
qM5h7FOfwvCFWG6exRCKX7z/wF3SD/AQf3h/ZnuL9D3fxWJ5L41FWGBjwDQb
MxZjKZZgBcphOUqhpOfatLbv4yme4A7ScR1XccX2LWXrIE5tWFu90A1NUAgF
bHyUfYGyHJoyiEFN8qujivah7cdoFFUfrO82hjfUe+W7OrGIE0tH4Bexi6hP
2UqoiHj16bjtacUv45KdI/LHYDhSMRQ3yb+FM7iAG/iELVrrz/iJvviId/iA
PrY+aIvWilmZCbTZHmUxXntpIsaipWJW5jdlb+t76Zpju1MGYTCqan7ykx+C
7+rnTe0F2xPfkKFYecrGaK0Xar2fk/9Ya2hrYGsRzbz15NkdCaSLI4WyA9Bf
3x+oubE56odkxUZiNEZhhOYxD7JhmGJWxu4su7taoY3mJ57vhCM/gpELYZTN
hxCEIxSf8AFf8R0Z9h3qD9W9kqoznqF4XtJ5fHdOOiMJXdFDYxyAFJtb9Ec/
/KXeVJ0BOzt2hnqTPwSJaI+O6IJOSiep/RooZ/sZFVDZd/eE3RdRpCNQWPkW
T0Al393nJRGJzMjku//DOuqt9dwdHG9n13f/C/tvFEcJ383FXLRFG7RAa1sr
Ysnaiykaa1ZkQxCCkQU5kUPp7GhH3VM8T9q8sQ75EBpwZ8TOShjpvAEXa0DZ
BETojNlZC9gPEH8o+w9+wK2drWEUIlW+M5LQBR3QCR2RiGBk1V3RHV0VT1SZ
XNonQfjru29Zv63/zXg21VzEat7iEKN1KaD7p6CdH+2vKNoZrPW3dbb1DtXY
Q5BZe9PGYmPKzjMncgTcXNucN0crneMj2O+5tY7U2v4HqCzzYg==
           "]]}],
        Lighting->{{"Ambient", 
           RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, {
          "Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{0, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}}, 
     {GrayLevel[0], Line3DBox[CompressedData["
1:eJwt0DtLwnEUBuCfFuTlX99Ba7cPEc3hUNqN6AMY2NoUodIQEQ0VtBRWRNIk
4hLYKtLS0AUiiaagpSlp6BkcnuVw3hfOyaxv5EuxEMIaI4yyQIF5iiyzNNxZ
ZYKIpGCCNBHj7Jpvs0OFN7754pI6d7RpcMM7H/T55JUX7unQ5ZGM/ix/PNHj
gWdy8RDixEgTkSJJgjGmyDLJNCtyRebIs8gWvwz44Zor6lywxz4HHNLijHNO
OeGIYxrcMssMTWruqFJmkxKp4e//AVAGL7w=
       "]]}},
    VertexNormals->CompressedData["
1:eJztWksKwkAM7W8tuHPrDVx5AS8gHkFw7R3UA3mDCl5EEMFjWJBuhMg0TTJJ
mk2ljzLNzHuTvIld7o+7Q1UUxaq71N1vPXts17d7e5ovXpvru/3eP9sePwM4
9vkmcRxvePWzPg2AQ89zx8nFC1f80Hpq4z1wnN608astnsAD59QzVd6Wzv9j
9yn1vk6t79B7veSZEjmvVP1g/ZKUvwrchl/1Eo/2+LXXF214oyweKT/sjd+S
aF5Y/yN9fqHSSehNZl65zrnU7/XKozedRF/FFz6Vfcddx7XxZSXOwG2uJzYe
r/VibD92aL+RWw/a9KZNz7n6ltA4VvSgbRwreC7etelnarj173Oo8qR1/UjV
Cyo9aNdV5KX/fOWqs1I+hPr/aG4c8vND+xLYcz3V+SJ1nNz9B6s4FS/e8yTX
OnDrVnpfUNUF6f7DWJyq3yu1X6R9cur3CdZ4p86r0n645+VivG6mxo/1RVZ1
KI1T6+cDDLavDg==
     "]], GraphicsComplex3DBox[CompressedData["
1:eJx1mX1o1WUUx+9255TpxsplztjcMgQhwhLBIrw36g97k4ggs1CzNJGkhWKi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    "], {{
      {RGBColor[0.880722, 0.611041, 0.142051], EdgeForm[None], Specularity[
        GrayLevel[1], 3], 
       StyleBox[GraphicsGroup3DBox[Polygon3DBox[CompressedData["
1:eJxNmHecz3Ucx79f++yOs8fd2XHuuDPDkXEdznayM8444844hfYgFQ2FJpV2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          "]]],
        Lighting->{{"Ambient", 
           RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, {
          "Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{0, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}}, 
     {GrayLevel[0], 
      Line3DBox[{24, 25, 165, 280, 271, 272, 281, 234, 211, 212, 230, 226, 
       227, 228, 232, 233, 236, 252, 254, 258, 259, 323, 320, 321, 311, 312, 
       337, 338, 340, 339, 315, 316, 334, 343, 371, 366, 364, 374, 157, 156, 
       161, 124, 126, 119, 118, 170, 173, 200, 198, 197, 180, 179, 183, 182, 
       188, 58, 57, 59, 108, 107, 81, 80, 90, 89, 93, 92, 94, 95, 96, 331, 
       105, 102, 103, 31, 24}]}},
    VertexNormals->CompressedData["
1:eJztyLENQFAUQNGHXvMnMIieVquT6IjOKDqz/CXMYQYKS0jObW5ymmkb5jIi
9iKien+sSzrHO9d9N6X2yvHFOeecc84555xzzjnnnHPOOeecc875H/0BJ1tM
zg==
     "]], GraphicsComplex3DBox[CompressedData["
1:eJx1mnlUlVUXxq+XGZlkkosMFzC/yNkyJ4rrl5lDmh/igCnibJpp5ZSakbqK
[encoded data, 5220 characters]
wyUkPNQGpy6puhD5w7wYHL2afAM/snFvwL6v9fj8H6Nm/J4=
    "], {{
      {RGBColor[0.880722, 0.611041, 0.142051], EdgeForm[None], Specularity[
        GrayLevel[1], 3], 
       StyleBox[GraphicsGroup3DBox[{Polygon3DBox[CompressedData["
1:eJwt0U8ow2Ecx/GHScJFaaymOKBcRomDslI7jUQcMGQO2hYupDnIhcPMYTlJ
2lbKn1zIn5SDnZS05aTIhRWShHCT9y+fw6vn+Tzfb8/v9/v+qvyT3RO5xpgm
2OBGG1oxh1mE0Qmv9lvYwRfKcowphx0P5HzWe9YSVofOK8iVcOIMKdxad1Db
xiamsIAwSqnZ1R8jr6ongiiWcETtGIfYJx9gDzXkWlTjGz96z3pqDXAhiw31
+6lFMAIP+QoZtJCbNYcLclrnBZoTW2PN7UX7d7zhA40cvOpZ13jCI+6o3ejb
6+BCP9qpdcGLZ3LW/M+wCMUotGZBrUM9a+R1xPGJXz03hhUkrDnTl8Ipzsm7
6s8jL7JGEWQf0sxnyNOa2wDZh0HMI6B9klpa9/eQezGEZXJGd/rQp+8apnai
nnFyCAEkyXG9W5B8qfMxjOpf/AFJSVId
           "]], Polygon3DBox[CompressedData["
1:eJxNmHd0l0UWhr9BmouAUlbEVSEgJSCKFKWDoFFWFIO0BREVIiJVbIfQm2LB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           "]], Polygon3DBox[CompressedData["
1:eJwt1Ftoj2EcB/C/GYlckBxnSAhpEyPk3JJYoonNzAxpE6KhKXIec4hcMNIM
MYcLM0SU4UKNHVAskjAkOc3pBvm87bn49D7/7/t7nvc59e+Tu3LWirhYLDaC
VixiCYvJZSGDGUQmGcwhiWRyyArvDlLCCco4Tj0HQruWR1xrEYulk811JnJX
vpw8HlDDbHkmOSwI9cfk1TzhHqUsk69iLQUUcptbnKSMmyxTm8pU8sO31pBN
Af3pxx21VaFPafRNMpjHfPKYSy01TCaVOqbpn8YGNlLIYY6GuV7gEB/UJpPE
J54zk1EkkhCNFa0jmg+veMFzKqkK7Wc00Mg73vKG13zXv4kGnvKeYfI2aMY+
MpovvORz1IcmOimYHuaQxkBGylMYy3jGcV9eHdb+kHo6y3uRSE8SmMCY0GcS
U+hIO9rSg+4M1X8EKQwP+/OORiq4zFuyKGI/m8K5tCKePcapi9ap/TXa67Af
rf3+4bmLpeFuF7OTG1RwkatcYZv6/HCftrOVHfIi9rE31vytnfJidrOFzdFZ
RnsY1t6b/ZySn6aSS2E96fIZ4Z6sZzV/+RbO4V90Vuq60YshdIn2mPZ0CO2u
9I3GV1/OT35HexvN23NduNsD2E6J/AjnOccZDnIgtM9SHr1T+5g//Arjtow1
/1fEExfu0n9fh4hx
           "]]}],
        Lighting->{{"Ambient", 
           RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, {
          "Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{0, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}}, 
     {GrayLevel[0], Line3DBox[CompressedData["
1:eJwt0L1KggEAheEvgiJpUJqiyQsQREIabAjCsLG1oVKixR8U1JYK2qJcpCms
pbkxhGoKG6KlpDFBcqgphW6gR2h4tjO8nGi2tFGcCIJgk2mmmGGRBEmWSLHC
KmnyFOnwzAtXtLjhmgvOafLGK12euOeWNg8EIibp8MglLX754psfhnzwTpce
I1IsM+CTPutkSLPGHQVKHHDIETvk2GWPBnX2qVKjTIVjTjnjZLyRXmOLbeLE
WCDELBHCzDH///Mf7AMuTg==
       "]]}},
    VertexNormals->CompressedData["
1:eJztWjsKwkAQXbVWCytLG1FT60G8gCBYWFl6AE/gPeytJDfIHWy1EbyAFtoI
QzLyJvt2s1XgEZZ5b76ZzWi9W27azrlny7nO+znbX+6D4znvjefbxeGWr4bF
ozhd86mAS+/Hik+U+mQfvF/xHF+8UP6VeLHx9aVPwrF6SvnFxpdNt4QnnKFv
stlZlw5dMntY9LGukyicjW8oeNP01PJl06dp9SEUv/iyJzO2xxcv9PeIVR59
7bSaH9jync0erd9DiVuU/lp7tPu0UOq8ds4PpX5az89SfWPtvyzfcWV92UpP
Nr8kvNl+rHsPbN0frfcS1ueX9XepLv36Mfb9jFXcsukTet+JPQ6t/cUyL/ma
k0M5nw0v41u1X7DxihW3znfUniHW/G3aPZfkX9Q+Vtrn1BXnLH0TZSeK1795
zbJf0sYnah/Odg7bPI+KH1S91caDFFeo/+VQe3vpfVRes/Uj67y21p/tvknC
X9Q7Kcg=
     "]], 
   {RGBColor[1, 0, 0], PointSize[0.05], Point3DBox[{0, 0, 0}]}},
  Axes->True,
  AxesLabel->{
    FormBox["x", TraditionalForm], 
    FormBox["y", TraditionalForm], 
    FormBox["z", TraditionalForm]},
  BoxRatios->{1, 1, 1},
  DisplayFunction->Identity,
  FaceGridsStyle->Automatic,
  Method->{"DefaultBoundaryStyle" -> Directive[
      GrayLevel[0.3]]},
  PlotRange->{{-10, 10}, {-10, 10}, {-10, 10}},
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02], 
    Scaled[0.02]},
  Ticks->{Automatic, Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.6672225063164797`*^9}]
}, {2}]],

Cell["\<\
H\[AAcute]rom \[AAcute]ltal\[AAcute]nos helyzet\[UDoubleAcute] s\[IAcute]kot \
kaptunk. L\[AAcute]that\[OAcute], hogy a h\[AAcute]rom s\[IAcute]k egy \
pontban metszi egym\[AAcute]st, \[IAcute]gy egy megold\[AAcute]sa van az \
egyenletrendszernek. Ebben az esetbe, ha csak egy megold\[AAcute]sa van az \
egyenletrendszernek, az biztos a trivi\[AAcute]lis megold\[AAcute]s.\
\>", "Text",
 CellChangeTimes->{{3.667223392516055*^9, 3.667223437092121*^9}},
 TextJustification->1.]
}, Open  ]],

Cell[CellGroupData[{

Cell["Van nem trivi\[AAcute]lis megold\[AAcute]sa is az egyenletrendszernek", \
"Subsection",
 CellChangeTimes->{3.6672225992937975`*^9}],

Cell[CellGroupData[{

Cell[TextData[{
 "\t1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+2\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0\n\t0\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+3\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+2\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0\n\t5\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "1"], TraditionalForm]]],
 "+4\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "2"], TraditionalForm]]],
 "+1\[CenterDot]",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "3"], TraditionalForm]]],
 "=0"
}], "Text",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.667222610770454*^9, 3.667222640720167*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"n51", "=", 
   RowBox[{"{", 
    RowBox[{"1", ",", "2", ",", "1"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sik51", "=", 
   RowBox[{"n51", ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], ")"}]}]}], ";"}]}], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6671366808089375`*^9, 3.667136682584039*^9}, {
  3.66713797008768*^9, 3.6671379929339867`*^9}, {3.667139089297423*^9, 
  3.6671390926546593`*^9}, {3.667139151260778*^9, 3.6671391551283627`*^9}, {
  3.6672226255522995`*^9, 3.667222640720167*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"n52", "=", 
   RowBox[{"{", 
    RowBox[{"0", ",", "3", ",", "2"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sik52", "=", 
   RowBox[{"n52", ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], ")"}]}]}], ";"}]}], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6671366843091373`*^9, 3.6671367006360717`*^9}, {
  3.667137972427814*^9, 3.667137998998334*^9}, {3.667139157531966*^9, 
  3.6671391813998957`*^9}, {3.6672226278394303`*^9, 3.667222640721167*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"n53", "=", 
   RowBox[{"{", 
    RowBox[{"5", ",", "4", ",", "1"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sik53", "=", 
   RowBox[{"n53", ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], ")"}]}]}], ";"}]}], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.6671367147988815`*^9, 3.6671367197911673`*^9}, {
  3.6671379779991326`*^9, 3.6671380042746353`*^9}, {3.667139163755118*^9, 
  3.6671391870696797`*^9}, {3.6672226299915533`*^9, 3.667222640721167*^9}}]
}, Closed]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"ContourPlot3D", "[", 
    RowBox[{
     RowBox[{"sik51", "\[Equal]", "0"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"Mesh", "\[Rule]", "None"}]}], "]"}], ",", " ", 
   RowBox[{"ContourPlot3D", "[", 
    RowBox[{
     RowBox[{"sik52", "\[Equal]", "0"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"Mesh", "\[Rule]", "None"}]}], "]"}], ",", " ", 
   RowBox[{"ContourPlot3D", "[", 
    RowBox[{
     RowBox[{"sik53", "\[Equal]", "0"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"y", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"z", ",", 
       RowBox[{"-", "10"}], ",", "10"}], "}"}], ",", 
     RowBox[{"Mesh", "\[Rule]", "None"}]}], "]"}], ",", 
   RowBox[{"AxesLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"x", ",", "y", ",", "z"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.6671380212376056`*^9, 3.667138039009622*^9}, {
  3.667139202529001*^9, 3.6671392612231765`*^9}}],

Cell[BoxData[
 Graphics3DBox[{GraphicsComplex3DBox[CompressedData["
1:eJx12nuQ12UVBvAfe8EFYV1kQRYEdyEzrMzSJg3HXRmbwUvWKI40FaAOSBSj
[encoded data, 4140 characters]
x5cXfPr44iaP/wMXioQf
    "], {{
      {RGBColor[0.880722, 0.611041, 0.142051], EdgeForm[None], Specularity[
        GrayLevel[1], 3], 
       StyleBox[GraphicsGroup3DBox[{Polygon3DBox[CompressedData["
1:eJxN1mWYVkUUwPGZdxeWhoXddWlwd2GJBaQbkZQOERAVWRqkGySku0MaJKUe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           "]], Polygon3DBox[CompressedData["
1:eJxNmAnUz1Uax+990Yvs+5Jdsi9FihZKpiSMpkKLaGMU7ZJSkgipVIpEFGqk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           "]]}],
        Lighting->{{"Ambient", 
           RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, {
          "Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{0, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}}, 
     {GrayLevel[0], Line3DBox[CompressedData["
1:eJwt0M8rA2AYB/B3O3LxI5xJ2SgiB0e5iOOOM0uy29riLMIfYcclNZZsl+Xk
sIu/QckmFxG1SWsO4iMOn57v09P79vSMbuYTuUgIYYMp4kwzQ9RgkD6+9N8M
yP30/j7iU+kyIg8zxIp+mVXOKVHkhDIFcmTYIss2O7zTpsUbrzxRpcIV19zy
QYexaAjjxJhkgn17LLHIGknWSZNigXlmmSPDLnscccAhPf6K8yI/06LNI00e
aHDHPRdcUuGMMjWKHFPghnrk7+ZpTv9v/wOwGjMz
       "]]}},
    VertexNormals->CompressedData["
1:eJztWsENwjAMrODLEPDnwb8thRUYAYk3LIi6ByMwBZUQj0ayEsd2cqH5UHGK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     "]], GraphicsComplex3DBox[CompressedData["
1:eJx1mW1o1XUUx+/uHtTpxtKbekfOTSNQKywKrLRdCUrTJEzJMNQ0bQwkSTOp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    "], {{
      {RGBColor[0.880722, 0.611041, 0.142051], EdgeForm[None], Specularity[
        GrayLevel[1], 3], 
       StyleBox[GraphicsGroup3DBox[Polygon3DBox[CompressedData["
1:eJxdmGeUVdUZhu+hVxk6wiACIyNNOkNx6CKC1KGHJsgwOAiCUmSEoZehCtKL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          "]]],
        Lighting->{{"Ambient", 
           RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, {
          "Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{0, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}}, 
     {GrayLevel[0], Line3DBox[CompressedData["
1:eJwt0L1KQgEAhuHjVRwbEgS3OjnE8Q7yZ4uzNBhZQjRpQSJ4E9EYBTZEg2lI
m0S1phlCQ0TYNQTONfQMDc/8fnzZ+mHSTAVBsMUSIRsUqVCmxDlndDnlhCm3
9LjmihEP3PPEI6+8MOGbBb/8cCk+oM8NM974Ys4n73wQkSemwB1DJox55oIK
ZYqUSNhknxZtjtihxi571KmyzQEZQtIc29qiQZMOOZbJsEbEKivErFP4//UP
NIcsXw==
       "]]}},
    VertexNormals->CompressedData["
1:eJzt2L0RglAMwPGIW9hRMYRb2NlyR+00WLPJc5BXaOdRMQIltQfx8vGn/BWQ
hCQcr+0ft6ERkXoSOct2vet96aa5PL/X6fL6FC0flV07fi9OnXHcjmebr2z5
4rH7R/t7ylzgkdxLP0edR+KnTzzGieP/9F/nQnsPHHV/5t3X/uR9UU8Lzv+s
rzpbywuP7dn6M2pe2dxa33KejOPx9rCXeSSenM/F8T3O+WdO5/zTl0ep5wqq
vCFF
     "]], GraphicsComplex3DBox[CompressedData["
1:eJx1mnl0zdcWx2/uvbmJROImuZHczLlqLEoTpTXkstQjFKt4eLyYaqjhNQtP
[encoded data, 5280 characters]
U3XOupxr5T1E7Jdk7p7yj6vy/+Ib/d7c8cWZVxL+j5Pn/Pt/AYT0XYA=
    "], {{
      {RGBColor[0.880722, 0.611041, 0.142051], EdgeForm[None], Specularity[
        GrayLevel[1], 3], 
       StyleBox[GraphicsGroup3DBox[{Polygon3DBox[CompressedData["
1:eJwt1Htoj1EYwPFzzqY1l367MDZT2+g36zeXP6eUS5hZLo1yydbMJmEbiZjc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           "]], Polygon3DBox[CompressedData["
1:eJxNl3mUzlUYx3+/l8ZIhuyGhmHG8lpCtlCItChRxpKlUlR2LVpobCkh4iCJ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           "]], Polygon3DBox[CompressedData["
1:eJwt1XlMz3Ecx/FvKSaS+0jMEbIUEWos5ibXMNew3IbKscw95CYjVzmXkGvO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           "]], 
          Polygon3DBox[{{507, 517, 529, 531, 533, 532}, {550, 515, 514, 553, 
           552, 555}}]}],
        Lighting->{{"Ambient", 
           RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, {
          "Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{0, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 2, 2}]}, {"Directional", 
           RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], 
           ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}}, 
     {GrayLevel[0], Line3DBox[CompressedData["
1:eJwt0L1KggEYBeCvhqKkpR9skegC1CwrFEkSWxy9AbElWgqaogKnbCnoBgpJ
h1qDnKUhpCHaWyMMooYiCgl6BIeHc6bDyzu7vl3cGgiCoMwgvb7AIkskWWaE
EHESrJClyAablPo7VZ745pkXrgw32CFDmhwFdtnjiEOqVNjngBuanHLMCWHH
TjLFOEMMEyVGgnnizDFKiAgzTPNl55M72jzwSI1zzrh1e4uIfi/bvR/pXfnH
hP4j33njg19e6VDngkuaXJMmRZ41Vhnr//8fkvstYg==
       "]]}},
    VertexNormals->CompressedData["
1:eJztW0tqAzEMnYxnHeiu21yhi14gFyg9QiHrHiI5UG4whV6kUAI9RobCbAaM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     "]]},
  Axes->True,
  AxesLabel->{
    FormBox["x", TraditionalForm], 
    FormBox["y", TraditionalForm], 
    FormBox["z", TraditionalForm]},
  BoxRatios->{1, 1, 1},
  DisplayFunction->Identity,
  FaceGridsStyle->Automatic,
  ImageSize->{378.17644870775376`, 418.9729341580966},
  ImageSizeRaw->Automatic,
  Method->{"DefaultBoundaryStyle" -> Directive[
      GrayLevel[0.3]]},
  PlotRange->{{-10, 10}, {-10, 10}, {-10, 10}},
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02], 
    Scaled[0.02]},
  Ticks->{Automatic, Automatic, Automatic},
  ViewPoint->{1.4093112056168868`, -1.5133778464107337`, 2.6783445296891677`},
  ViewVertical->{-0.07720219367270356, 0.29309206989971376`, 
   0.9529621502735687}]], "Output",
 CellChangeTimes->{
  3.6672226322636833`*^9},ImageCache->GraphicsData["CompressedBitmap", "\<\
[encoded data, 11340 characters]
mQwdYlxeWKi2VyPH70GRueIx7z35//8ujvhfAmz7HQ==\
\>"]]
}, {2}]],

Cell["\<\
A h\[AAcute]rom s\[IAcute]k egy egyenesben metszi egym\[AAcute]st, \
\[IAcute]gy teh\[AAcute]t v\[EAcute]gtelen sok megold\[AAcute]sa van az \
egyenletrendszernek, \[EAcute]s egy szabad v\[AAcute]ltoz\[OAcute]ja minden \
megold\[AAcute]snak.\
\>", "Text",
 CellChangeTimes->{{3.6672234489361424`*^9, 3.667223485342198*^9}},
 TextJustification->1.]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\[CapitalODoubleDot]sszegz\[EAcute]s:", "Section",
 CellChangeTimes->{{3.665151920652933*^9, 3.6651519262066464`*^9}, {
  3.666548138244272*^9, 3.6665481399654245`*^9}},
 TextJustification->1.,
 FontWeight->"Bold",
 FontSlant->"Italic"],

Cell["\<\
L\[AAcute]thattuk, hogy az egyenletrendszerek oszlopvektorai alkalmasak line\
\[AAcute]ris homog\[EAcute]n \[EAcute]s inhomog\[EAcute]n egyenletrendszerek \
megold\[AAcute]s\[AAcute]nak grafikus \
illusztr\[AAcute]ci\[OAcute]j\[AAcute]ra. A grafikus \[AAcute]br\[AAcute]zol\
\[AAcute]s alapja a vektorok line\[AAcute]ris kombin\[AAcute]ci\[OAcute]ja. \
Ekkor a skal\[AAcute]rok v\[AAcute]ltoztat\[AAcute]s\[AAcute]val keress\
\[UDoubleDot]k a megold\[AAcute]st. A megfelel\[ODoubleAcute] sz\[AAcute]mh\
\[AAcute]rmasok adj\[AAcute]k a keresett ismeretleneket.

Inhomog\[EAcute]n egyenletrendszerekn\[EAcute]l a f\[UDoubleDot]ggetlen \
egyenletek sz\[AAcute]ma \[EAcute]s a v\[AAcute]ltoz\[OAcute]k sz\[AAcute]ma \
k\[ODoubleDot]zti kapcsolat v\[AAcute]ltoztat\[AAcute]s\[AAcute]val 3 esetet \
vizsg\[AAcute]ltunk:
\t1. A f\[UDoubleDot]ggetlen egyenletek sz\[AAcute]ma \[EAcute]s a \
v\[AAcute]ltoz\[OAcute]k sz\[AAcute]ma egyenl\[ODoubleAcute]: Az \
egyenletrendszernek ekkor egy megold\[AAcute]sa van.
\t2. A f\[UDoubleDot]ggetlen egyenletek sz\[AAcute]ma 1-gyel kisebb, mint a v\
\[AAcute]ltoz\[OAcute]k sz\[AAcute]ma: Az egyenletrendszernek \
v\[EAcute]gtelen sok megold\[AAcute]sa van, valamint egy szabad \
v\[AAcute]ltoz\[OAcute]ja.
\t3. A f\[UDoubleDot]ggetlen egyenletek sz\[AAcute]ma 2-vel kisebb, mint a v\
\[AAcute]ltoz\[OAcute]k sz\[AAcute]ma: Az egyenletrendszernek \
v\[EAcute]gtelen sok megold\[AAcute]sa van, valamint k\[EAcute]t szabad v\
\[AAcute]ltoz\[OAcute]ja.

Ezen k\[IAcute]v\[UDoubleDot]l vizsg\[AAcute]ltuk a homog\[EAcute]n \
egyenletrendszerek k\[EAcute]t csoportj\[AAcute]t:
\t1. Csak trivi\[AAcute]lis megold\[AAcute]sa van az egyenletrendszernek.
\t2. A trivi\[AAcute]lis megold\[AAcute]son k\[IAcute]v\[UDoubleDot]l m\
\[AAcute]sik megold\[AAcute]sa is van az egyenletrendszernek.\
\>", "Text",
 CellChangeTimes->{
  3.6665449299327464`*^9, {3.666548144154213*^9, 3.6665481447306175`*^9}, {
   3.666548177277293*^9, 3.6665486106702256`*^9}, {3.6665486985608163`*^9, 
   3.6665487093319964`*^9}, {3.6665487748016443`*^9, 3.666548789503441*^9}, {
   3.666548901710245*^9, 3.666548914155546*^9}, {3.666548957208249*^9, 
   3.666548986710917*^9}},
 TextJustification->1.]
}, Open  ]],

Cell[CellGroupData[{

Cell["Forr\[AAcute]sok:", "Section",
 CellChangeTimes->{{3.665151920652933*^9, 3.6651519262066464`*^9}},
 TextJustification->1.,
 FontWeight->"Bold",
 FontSlant->"Italic"],

Cell["\<\
Freud R\[OAcute]bert (2007): Line\[AAcute]ris algebra. ELTE E\[ODoubleDot]tv\
\[ODoubleDot]s Kiad\[OAcute], Budapest\
\>", "Text",
 CellChangeTimes->{3.6665449299327464`*^9},
 TextJustification->1.],

Cell["", "Text",
 CellChangeTimes->{{3.665151936145299*^9, 3.665151950372808*^9}, {
   3.6651519973292055`*^9, 3.665152023174492*^9}, {3.6651520579147234`*^9, 
   3.6651521038064117`*^9}, 3.6658239980136385`*^9},
 TextJustification->1.]
}, Open  ]]
},
WindowToolbars->"EditBar",
WindowSize->{1358, 639},
WindowMargins->{{Automatic, 0}, {Automatic, 0}},
DockedCells->FEPrivate`FrontEndResource[
 "NotebookTemplatingExpressions", "AuthoringDockedCell"],
ShowSelection->True,
TaggingRules->{"NotebookTemplateVersion" -> 1., "NotebookTemplate" -> True},
CellContext->Notebook,
FrontEndVersion->"9.0 for Microsoft Windows (64-bit) (January 25, 2013)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[557, 20, 718, 15, 285, "Section"],
Cell[CellGroupData[{
Cell[1300, 39, 290, 6, 49, "Section"],
Cell[1593, 47, 2000, 70, 125, "Text"],
Cell[3596, 119, 598, 11, 49, "Text"],
Cell[4197, 132, 7166, 247, 564, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[11400, 384, 250, 5, 79, "Section"],
Cell[CellGroupData[{
Cell[11675, 393, 316, 6, 44, "Subsection"],
Cell[11994, 401, 435, 11, 87, "Text"],
Cell[CellGroupData[{
Cell[12454, 416, 2712, 79, 92, "Input"],
Cell[15169, 497, 452, 10, 382, "Output"]
}, {2}]],
Cell[15633, 510, 2653, 93, 222, "Text"],
Cell[18289, 605, 428, 11, 87, "Text"],
Cell[18720, 618, 2581, 93, 387, "Text"],
Cell[CellGroupData[{
Cell[21326, 715, 2919, 83, 92, "Input"],
Cell[24248, 800, 10058, 168, 375, 434, 9, "CachedBoxData", "BoxData", "Output"]
}, {2}]],
Cell[34318, 971, 1198, 35, 106, "Text"],
Cell[CellGroupData[{
Cell[35541, 1010, 4800, 130, 132, "Input"],
Cell[40344, 1142, 3433, 70, 524, "Output"]
}, {2}]],
Cell[43789, 1215, 472, 11, 87, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[44298, 1231, 365, 8, 44, "Subsection"],
Cell[44666, 1241, 420, 8, 30, "Text"],
Cell[CellGroupData[{
Cell[45111, 1253, 470, 10, 35, "Subsubsection"],
Cell[45584, 1265, 326, 7, 30, "Text"],
Cell[45913, 1274, 1015, 41, 68, "Text"],
Cell[46931, 1317, 324, 6, 30, "Text"],
Cell[CellGroupData[{
Cell[47280, 1327, 3724, 101, 212, "Input"],
Cell[51007, 1430, 3214, 64, 524, "Output"]
}, {2}]],
Cell[54233, 1497, 716, 23, 39, "Text"],
Cell[CellGroupData[{
Cell[54974, 1524, 276, 10, 58, "Input"],
Cell[55253, 1536, 192, 6, 46, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[55494, 1548, 455, 10, 35, "Subsubsection"],
Cell[55952, 1560, 278, 7, 68, "Text"],
Cell[56233, 1569, 1115, 42, 68, "Text"],
Cell[57351, 1613, 475, 10, 68, "Text"],
Cell[CellGroupData[{
Cell[57851, 1627, 3550, 96, 192, "Input"],
Cell[61404, 1725, 3187, 63, 524, "Output"]
}, {2}]],
Cell[64603, 1791, 2380, 73, 93, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[67020, 1869, 352, 8, 35, "Subsubsection"],
Cell[67375, 1879, 249, 5, 30, "Text"],
Cell[67627, 1886, 969, 40, 68, "Text"],
Cell[68599, 1928, 410, 8, 49, "Text"],
Cell[CellGroupData[{
Cell[69034, 1940, 3562, 98, 192, "Input"],
Cell[72599, 2040, 3185, 63, 532, "Output"]
}, {2}]],
Cell[75796, 2106, 1914, 60, 87, "Text"],
Cell[77713, 2168, 321, 9, 46, "Input"],
Cell[78037, 2179, 414, 7, 30, "Text"],
Cell[78454, 2188, 2415, 111, 106, "Text"],
Cell[80872, 2301, 207, 3, 30, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[81116, 2309, 278, 5, 36, "Subsubsection"],
Cell[81397, 2316, 828, 22, 68, "Text"],
Cell[82228, 2340, 1015, 41, 68, "Text"],
Cell[83246, 2383, 470, 9, 30, "Text"],
Cell[CellGroupData[{
Cell[83741, 2396, 2908, 79, 152, "Input"],
Cell[86652, 2477, 2973, 59, 522, "Output"]
}, {2}]],
Cell[89637, 2539, 793, 22, 30, "Text"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[90479, 2567, 233, 5, 44, "Subsection"],
Cell[90715, 2574, 381, 8, 30, "Text"],
Cell[91099, 2584, 964, 40, 68, "Text"],
Cell[92066, 2626, 281, 6, 30, "Text"],
Cell[CellGroupData[{
Cell[92372, 2636, 2908, 79, 152, "Input"],
Cell[95283, 2717, 2973, 59, 534, "Output"]
}, {2}]],
Cell[98268, 2779, 2378, 78, 93, "Text"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[100695, 2863, 196, 3, 79, "Section"],
Cell[100894, 2868, 1277, 20, 125, "Text"],
Cell[CellGroupData[{
Cell[102196, 2892, 152, 2, 52, "Subsection"],
Cell[CellGroupData[{
Cell[102373, 2898, 271, 5, 34, "Subsubsection"],
Cell[CellGroupData[{
Cell[102669, 2907, 1021, 41, 68, "Text",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[103693, 2950, 631, 17, 52, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[104327, 2969, 631, 17, 52, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[104961, 2988, 633, 17, 52, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}]
}, Closed]],
Cell[CellGroupData[{
Cell[105631, 3010, 2121, 57, 152, "Input"],
Cell[107755, 3069, 44508, 759, 420, 30002, 519, "CachedBoxData", "BoxData", \
"Output"]
}, {2}]],
Cell[152275, 3831, 365, 7, 30, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[152677, 3843, 260, 5, 34, "Subsubsection"],
Cell[CellGroupData[{
Cell[152962, 3852, 1019, 41, 68, "Text",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[153984, 3895, 713, 18, 52, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[154700, 3915, 684, 17, 52, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[155387, 3934, 730, 18, 52, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}]
}, Closed]],
Cell[CellGroupData[{
Cell[156154, 3957, 1884, 49, 112, "Input"],
Cell[158041, 4008, 22929, 402, 410, "Output"]
}, {2}]],
Cell[180982, 4413, 469, 8, 49, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[181488, 4426, 257, 5, 34, "Subsubsection"],
Cell[CellGroupData[{
Cell[181770, 4435, 1024, 41, 68, "Text",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[182797, 4478, 760, 18, 52, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[183560, 4498, 734, 18, 52, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[184297, 4518, 783, 20, 52, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}]
}, Closed]],
Cell[CellGroupData[{
Cell[185117, 4543, 1936, 50, 112, "Input"],
Cell[187056, 4595, 29474, 515, 420, "Output"]
}, {2}]],
Cell[216542, 5113, 389, 7, 30, "Text"]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[216992, 5127, 114, 1, 79, "Section"],
Cell[CellGroupData[{
Cell[217131, 5132, 182, 2, 43, "Subsection"],
Cell[CellGroupData[{
Cell[217338, 5138, 1023, 41, 68, "Text",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[218364, 5181, 838, 19, 52, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[219205, 5202, 830, 19, 52, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[220038, 5223, 830, 19, 52, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}]
}, Closed]],
Cell[CellGroupData[{
Cell[220905, 5247, 2299, 59, 72, "Input"],
Cell[223207, 5308, 30214, 523, 420, "Output"]
}, {2}]],
Cell[253433, 5834, 486, 8, 49, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[253956, 5847, 137, 2, 43, "Subsection"],
Cell[CellGroupData[{
Cell[254118, 5853, 991, 40, 68, "Text",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[255112, 5895, 730, 18, 52, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[255845, 5915, 680, 17, 52, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[256528, 5934, 684, 17, 52, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}]
}, Closed]],
Cell[CellGroupData[{
Cell[257249, 5956, 1633, 46, 72, "Input"],
Cell[258885, 6004, 43101, 738, 434, 31424, 545, "CachedBoxData", "BoxData", \
"Output"]
}, {2}]],
Cell[301998, 6745, 357, 7, 30, "Text"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[302404, 6758, 242, 5, 79, "Section"],
Cell[302649, 6765, 2209, 38, 220, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[304895, 6808, 171, 4, 79, "Section"],
Cell[305069, 6814, 208, 5, 30, "Text"],
Cell[305280, 6821, 236, 4, 30, "Text"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)
