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Das merkt man bei den ersten beiden Kommandos noch \ nicht, denn sie werden komponentenweise ausgef\[UDoubleDot]hrt." }], "SmallText", CellChangeTimes->{{3354640846.20261, 3354640898.03258}, {3356621444.48362, 3356621485.61496}}], Cell[BoxData[ RowBox[{ RowBox[{ OverscriptBox["a", "\[RightVector]"], "=", RowBox[{"(", GridBox[{ {"a1"}, {"a2"}, {"a3"} }], ")"}]}], ";", " ", RowBox[{ OverscriptBox["b", "\[RightVector]"], "=", RowBox[{"(", GridBox[{ {"b1"}, {"b2"}, {"b3"} }], ")"}]}], ";", " ", RowBox[{ OverscriptBox["c", "\[RightVector]"], "=", RowBox[{"{", RowBox[{"c1", ",", "c2", ",", "c3"}], "}"}]}], ";"}]], "Input", CellChangeTimes->{{3.35464038821048*^9, 3.35464042579998*^9}, { 3.35464051440265*^9, 3.35464052344683*^9}, {3.3546406081391*^9, 3.3546406780396*^9}, {3.35662132562093*^9, 3.35662135104775*^9}, { 3.35662150526405*^9, 3.35662151869813*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"{", RowBox[{ OverscriptBox["a", "\[RightVector]"], ",", OverscriptBox["b", "\[RightVector]"], ",", " ", OverscriptBox["c", "\[RightVector]"]}], "}"}]], "Input", CellChangeTimes->{{3.35662152318402*^9, 3.35662154033244*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "a1", "}"}], ",", RowBox[{"{", "a2", "}"}], ",", RowBox[{"{", "a3", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "b1", "}"}], ",", RowBox[{"{", "b2", "}"}], ",", RowBox[{"{", "b3", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"c1", ",", "c2", ",", "c3"}], "}"}]}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{" ", RowBox[{"MatrixForm", "/@", RowBox[{"{", RowBox[{ OverscriptBox["a", "\[RightVector]"], ",", OverscriptBox["b", "\[RightVector]"], ",", " ", OverscriptBox["c", "\[RightVector]"]}], "}"}]}]}]], "Input", CellChangeTimes->{{3.35464068387677*^9, 3.3546407242058*^9}, { 3.3566215472949*^9, 3.35662155652375*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"a1"}, {"a2"}, {"a3"} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]], ",", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"b1"}, {"b2"}, {"b3"} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]], ",", TagBox[ RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"c1"}, {"c2"}, {"c3"} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Column], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"VectorQ", "[", OverscriptBox["a", "\[RightVector]"], "]"}]], "Input", CellChangeTimes->{{3.35662156060063*^9, 3.35662156168775*^9}}], Cell[BoxData["False"], "Output"] }, Open ]], Cell["\<\ Einspaltige Matrizen k\[ODoubleDot]nnen wie Vektoren addiert und skalar \ vervielfacht werden. Das Ergebnis ist wieder eine einspaltige Matrix.\ \>", "SmallText", CellChangeTimes->{{3.3546409824036*^9, 3.35464102116419*^9}, { 3.35464105934856*^9, 3.35464108680613*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ OverscriptBox["a", "\[RightVector]"], "+", OverscriptBox["b", "\[RightVector]"]}], " ", "//", "MatrixForm"}]], "Input",\ CellChangeTimes->{{3.3566215659475*^9, 3.35662157047832*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"a1", "+", "b1"}]}, { RowBox[{"a2", "+", "b2"}]}, { RowBox[{"a3", "+", "b3"}]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output"] }, Open ]], Cell["\<\ Selbst die Summe einer einspaltigen Matrix und eines Vektors kann gebildet \ werden. Das Ergebnis ist eine einspaltige Matrix.\ \>", "SmallText", CellChangeTimes->{{3.35464109245615*^9, 3.35464115407025*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ OverscriptBox["a", "\[RightVector]"], "+", OverscriptBox["c", "\[RightVector]"]}]], "Input", CellChangeTimes->{{3.35464104772817*^9, 3.35464104895804*^9}, { 3.35662137539683*^9, 3.356621376041*^9}, {3.35662157705807*^9, 3.35662158201651*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"a1", "+", "c1"}], "}"}], ",", RowBox[{"{", RowBox[{"a2", "+", "c2"}], "}"}], ",", RowBox[{"{", RowBox[{"a3", "+", "c3"}], "}"}]}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "MatrixForm"}]], "Input", CellChangeTimes->{ 3.35464113026268*^9, {3.35662136656316*^9, 3.35662136966506*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"a1", "+", "c1"}]}, { RowBox[{"a2", "+", "c2"}]}, { RowBox[{"a3", "+", "c3"}]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output"] }, Open ]], Cell[TextData[{ "Als einspaltige Matrizen sind ", Cell[BoxData[ OverscriptBox["a", "\[RightVector]"]]], " und ", Cell[BoxData[ RowBox[{" ", OverscriptBox["b", "\[RightVector]"]}]]], " nicht verkettet - deshalb endet dieses Dot-Kommando mit einer \ Fehlermeldung. W\[ADoubleDot]ren es Vektoren, w\[UDoubleDot]rde es als \ Skalarprodukt interpretiert und ausgef\[UDoubleDot]hrt." }], "SmallText", CellChangeTimes->{{3.35662160354959*^9, 3.35662163522957*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ OverscriptBox["a", "\[RightVector]"], " ", ".", " ", OverscriptBox["b", "\[RightVector]"]}]], "Input", CellChangeTimes->{{3.35662158855663*^9, 3.35662159356681*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"Dot", "::", "\<\"dotsh\"\>"}], RowBox[{ ":", " "}], "\<\"Tensors \\!\\({\\(\\({a1}\\)\\), \\(\\({a2}\\)\\), \ \\(\\({a3}\\)\\)}\\) and \\!\\({\\(\\({b1}\\)\\), \\(\\({b2}\\)\\), \ \\(\\({b3}\\)\\)}\\) have incompatible shapes.\"\>"}]], "Message", "MSG"], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "a1", "}"}], ",", RowBox[{"{", "a2", "}"}], ",", RowBox[{"{", "a3", "}"}]}], "}"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", "b1", "}"}], ",", RowBox[{"{", "b2", "}"}], ",", RowBox[{"{", "b3", "}"}]}], "}"}]}]], "Output"] }, Open ]], Cell["\<\ Dasselbe gilt f\[UDoubleDot]r das Vektorprodukt, das ebenfalls nur f\ \[UDoubleDot]r Vektoren, nicht aber f\[UDoubleDot]r einspaltige Matrizen \ definiert ist. \ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ OverscriptBox["a", "\[RightVector]"], " ", "\[Cross]", OverscriptBox["b", "\[RightVector]"], " "}]], "Input", CellChangeTimes->{{3.35662164884991*^9, 3.35662166070606*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"Cross", "::", "\<\"nonn1\"\>"}], RowBox[{ ":", " "}], "\<\"The arguments are expected to be vectors of equal length, \ and the number of arguments is expected to be 1 less than their \ length.\"\>"}]], "Message", "MSG"], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "a1", "}"}], ",", RowBox[{"{", "a2", "}"}], ",", RowBox[{"{", "a3", "}"}]}], "}"}], "\[Cross]", RowBox[{"{", RowBox[{ RowBox[{"{", "b1", "}"}], ",", RowBox[{"{", "b2", "}"}], ",", RowBox[{"{", "b3", "}"}]}], "}"}]}]], "Output"] }, Open ]], Cell[TextData[{ "Verkettet sind hingegen ", Cell[BoxData[ RowBox[{ OverscriptBox["a", "\[RightVector]"], " "}]], "Input", CellChangeTimes->{{3.35662158855663*^9, 3.35662159356681*^9}}, FontWeight->"Plain"], "und die zu ", Cell[BoxData[ RowBox[{ OverscriptBox["b", "\[RightVector]"], " "}]], "Input", CellChangeTimes->{{3.35662158855663*^9, 3.35662159356681*^9}}, FontWeight->"Plain"], "transponierte Matrix, und zwar in beiden Reihenfolgen. \nIm ersten Fall \ ergibt sich eine 3\[Times]3-Matrix, deren Eintr\[ADoubleDot]ge die paarweisen \ Produkte sind; im zweiten Fall eine 1\[Times]1-Matrix mit dem Skalarprodukt \ als Eintrag." }], "SmallText", CellChangeTimes->{{3.35662204098694*^9, 3.35662215045451*^9}, { 3.35662224668827*^9, 3.35662225529259*^9}, {3.35662239014366*^9, 3.35662243188979*^9}, {3.35662287529611*^9, 3.35662287975284*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ OverscriptBox["a", "\[RightVector]"], " ", ".", RowBox[{"Transpose", "[", " ", OverscriptBox["b", "\[RightVector]"], "]"}]}], "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.3566219358723*^9, 3.35662198503249*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"a1", " ", "b1"}], RowBox[{"a1", " ", "b2"}], RowBox[{"a1", " ", "b3"}]}, { RowBox[{"a2", " ", "b1"}], RowBox[{"a2", " ", "b2"}], RowBox[{"a2", " ", "b3"}]}, { RowBox[{"a3", " ", "b1"}], RowBox[{"a3", " ", "b2"}], RowBox[{"a3", " ", "b3"}]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Transpose", "[", " ", OverscriptBox["b", "\[RightVector]"], " ", "]"}], ".", OverscriptBox["a", "\[RightVector]"]}], "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.35662199819489*^9, 3.35662200939643*^9}, { 3.3566223637578*^9, 3.35662236829544*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ RowBox[{"a1", " ", "b1"}], "+", RowBox[{"a2", " ", "b2"}], "+", RowBox[{"a3", " ", "b3"}]}]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output"] }, Open ]], Cell["\<\ Auf die Kombination von Matrix und Vektor wirkt . nicht als Skalarprodukt, \ sondern als Produkt von Matrix und Vektor. Daf\[UDoubleDot]r \ m\[UDoubleDot]ssen beide verkettet sein. 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RowBox[{"Solve", "::", "\<\"svars\"\>"}], RowBox[{ ":", " "}], "\<\"Equations may not give solutions for all \\\"solve\\\" \ variables.\"\>"}]], "Message", "MSG"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"x1", "\[Rule]", RowBox[{ FractionBox["7", "6"], "+", FractionBox[ RowBox[{"2", " ", "x4"}], "3"]}]}], ",", RowBox[{"x2", "\[Rule]", RowBox[{ FractionBox["1", "6"], "-", FractionBox["x4", "3"]}]}], ",", RowBox[{"x3", "\[Rule]", RowBox[{ FractionBox["25", "6"], "-", FractionBox["x4", "3"]}]}]}], "}"}], "}"}]], "Output"] }, Open ]], Cell[TextData[{ "Die Solve-Funktion gibt als Anwort eine Substitutionsliste \ zur\[UDoubleDot]ck, aus der sich die allgemeine L\[ODoubleDot]sung durch \ Substitution in die einspaltige Matrix ", StyleBox["x", FontWeight->"Bold"], " gewinnen l\[ADoubleDot]sst. Beachten Sie, dass die L\[ODoubleDot]sung eine \ einelementige ", StyleBox["Menge", FontSlant->"Italic"], " ist." }], "SmallText", CellChangeTimes->{{3.35865279637057*^9, 3.35865294148766*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"MatrixForm", "/@", RowBox[{"(", RowBox[{ RowBox[{"x", "/.", "sol"}], "/.", RowBox[{"x4", "\[Rule]", "t"}]}], ")"}]}]], "Input", CellChangeTimes->{{3.35857180901215*^9, 3.35857187356302*^9}, { 3.35857404024004*^9, 3.35857406112246*^9}, {3.35865443553511*^9, 3.35865448063429*^9}}], Cell[BoxData[ RowBox[{"{", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{ FractionBox["7", "6"], "+", FractionBox[ RowBox[{"2", " ", "t"}], "3"]}]}, { RowBox[{ FractionBox["1", "6"], "-", FractionBox["t", "3"]}]}, { RowBox[{ FractionBox["25", "6"], "-", FractionBox["t", "3"]}]}, {"t"} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]], "}"}]], "Output"] }, Open ]], Cell[TextData[{ "Gelegentlich muss die Menge der Variablen angegeben werden, etwa wenn die \ Ausdr\[UDoubleDot]cke noch weitere Parameter enthalten. Diese \ m\[UDoubleDot]ssen dazu aus ", StyleBox["x", FontWeight->"Bold"], " extrahiert werden. " }], "SmallText", CellChangeTimes->{{3.35865300590346*^9, 3.35865308382804*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"vars", "=", RowBox[{"Flatten", "[", "x", "]"}]}], "\n", RowBox[{"sol", "=", RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"mat", ".", "x"}], "\[Equal]", "b"}], ",", "vars"}], "]"}]}]}], "Input", CellChangeTimes->{{3.35857326385022*^9, 3.35857327075319*^9}, { 3.35857330672971*^9, 3.35857331245965*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"x1", ",", "x2", ",", "x3", ",", "x4"}], "}"}]], "Output"], Cell[BoxData[ RowBox[{ RowBox[{"Solve", "::", "\<\"svars\"\>"}], RowBox[{ ":", " "}], "\<\"Equations may not give solutions for all \\\"solve\\\" \ variables.\"\>"}]], "Message", "MSG"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"x1", "\[Rule]", RowBox[{ FractionBox["7", "6"], "+", FractionBox[ RowBox[{"2", " ", "x4"}], "3"]}]}], ",", RowBox[{"x2", "\[Rule]", RowBox[{ FractionBox["1", "6"], "-", FractionBox["x4", "3"]}]}], ",", RowBox[{"x3", "\[Rule]", RowBox[{ FractionBox["25", "6"], "-", FractionBox["x4", "3"]}]}]}], "}"}], "}"}]], "Output"] }, Open ]], Cell[TextData[{ "Lineare Gleichungssysteme lassen sich auch mit dem Kommando ", StyleBox["LinearSolve", FontWeight->"Bold"], " l\[ODoubleDot]sen. Dieses ist besonders dann angebracht, wenn es sich um \ gro\[SZ]e lineare Gleichungssysteme handelt oder ein und dasselbe System mit \ vielen verschiedenen rechten Seiten gel\[ODoubleDot]st werden soll. \nEs gibt \ zwei Aufrufvarianten des Kommandos ", StyleBox["LinearSolve", FontWeight->"Bold"], ". Die erste Variante ", StyleBox["LinearSolve[mat] ", FontWeight->"Bold"], "bekommt nur die Koeffizientenmatrix als Parameter \[UDoubleDot]bergeben \ und generiert daraus ein ", StyleBox["LinearSolveFunction", FontWeight->"Bold"], "-Objekt." }], "SmallText", CellChangeTimes->{{3.35865309927189*^9, 3.35865340484957*^9}, { 3.3586534398062*^9, 3.35865372430013*^9}, 3.35865386937932*^9, 3.35865489250533*^9, {3.35865499438126*^9, 3.35865499584768*^9}, { 3.35865517295396*^9, 3.35865519226922*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"lsol", "=", RowBox[{"LinearSolve", "[", "mat", "]"}]}]], "Input", CellChangeTimes->{ 3.35857020049414*^9, {3.35857271914962*^9, 3.35857272012829*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"LinearSolve", "::", "\<\"sqmat1\"\>"}], RowBox[{ ":", " "}], "\<\"The matrix \\!\\({\\(\\({1, 2, 3, 1}\\)\\), \\(\\({3, 1, \ 2, \\(\\(-1\\)\\)}\\)\\), \\(\\({2, 3, 1, 0}\\)\\)}\\) is not square so a \ factorization will not be saved.\"\>"}]], "Message", "MSG"], Cell[BoxData[ TagBox[ RowBox[{"LinearSolveFunction", "[", RowBox[{ RowBox[{"{", RowBox[{"3", ",", "4"}], "}"}], ",", "\<\"<>\"\>"}], "]"}], False, Editable->False]], "Output"] }, Open ]], Cell[TextData[{ "Es handelt sich dabei wie bei einer ", StyleBox["InterpolatingFunction", FontWeight->"Bold"], " um eine namenlose Funktion, von der auch die Berechnungsvorschrift nicht \ explizit bekannt ist. Sie berechnet zu einer vorgegebenen rechten Seite ", StyleBox["b", FontWeight->"Bold"], " eine L\[ODoubleDot]sung des Gleichungssystems." }], "SmallText", CellChangeTimes->{{3.35865309927189*^9, 3.35865340484957*^9}, { 3.3586534398062*^9, 3.35865372430013*^9}, 3.35865386937932*^9, 3.35865489250533*^9, {3.35865499438126*^9, 3.35865499584768*^9}, { 3.35865518093976*^9, 3.35865520311125*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"lsol", "[", "b", "]"}], "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.35857272352404*^9, 3.35857274042781*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { FractionBox["7", "6"]}, { FractionBox["1", "6"]}, { FractionBox["25", "6"]}, {"0"} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output"] }, Open ]], Cell[TextData[{ "Die zweite Aufrufvariante ", StyleBox["LinearSolve[mat,b] ", FontWeight->"Bold"], "bekommt als zweiten Parameter die rechte Seite \[UDoubleDot]bergeben und \ entspricht dem Aufruf ", StyleBox["LinearSolve[mat][b]. 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Da die allgemeine L\[ODoubleDot]sung \ eines linearen Gleichungssystems sich zusammensetzt aus einer solchen \ speziellen L\[ODoubleDot]sung und der allgemeinen L\[ODoubleDot]sung des \ zugeh\[ODoubleDot]rigen homogenen linearen Gleichungssystems, bleibt eine \ Basis des L\[ODoubleDot]sungsraums des homogenen Systems zu bestimmen. Dies \ kann mit dem Kommando ", StyleBox["NullSpace", FontWeight->"Bold"], " erfolgen. 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