(* Content-type: application/vnd.wolfram.cdf.text *) (*** Wolfram CDF File ***) (* http://www.wolfram.com/cdf *) (* CreatedBy='Mathematica 9.0' *) (*************************************************************************) (* *) (* The Mathematica License under which this file was created prohibits *) (* restricting third parties in receipt of this file from republishing *) (* or redistributing it by any means, including but not limited to *) (* rights management or terms of use, without the express consent of *) (* Wolfram Research, Inc. 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Universidad de Salamanca. \ \>", "Text"], Cell["Actualizado : 2013-05-02", "ItemParagraph"], Cell[TextData[{ "En este tutorial se hace una introducci\[OAcute]n a las operaciones con \ matrices y determinantes. Se ha elaborado integramente utilizando el programa \ ", StyleBox["Mathematica", FontSlant->"Italic"], " (disponible para todos los alumnos y profesorado de la Universidad de \ Salamanca). 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En el ejemplo lo que se hace es construir una nueva matriz A1 \ donde la fila 1 (F1) es identica a F1 de A, la fila F2 de A1 se obtiene \ extrayendo la fila F2 de A y restandole la fila F1 de A multiplicada por 2 \ (esto es: ", StyleBox["F2-> F2-2 F1", "Input"], " ) de la misma forma construimos la F3 de A1 extrayendo F3 de A y l \ restamos F1 de A ( es decir, ", StyleBox["F3-F1", "Input"], ")" }], "Subitem"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"A1", "=", RowBox[{"{", RowBox[{ RowBox[{"A", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{ RowBox[{"A", "[", RowBox[{"[", "2", "]"}], "]"}], "-", " ", RowBox[{"2", " ", RowBox[{"A", "[", RowBox[{"[", "1", "]"}], "]"}]}]}], ",", RowBox[{ RowBox[{"A", "[", RowBox[{"[", "3", "]"}], "]"}], "-", RowBox[{"A", "[", RowBox[{"[", "1", "]"}], "]"}]}]}], "}"}]}]], "Input"], Cell[BoxData[ FormBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "4", RowBox[{"-", "1"}]}, {"0", RowBox[{"-", "3"}], "5"}, {"0", "6", RowBox[{"-", "10"}]} }, 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la soluci\[OAcute]n." }], "Text"], Cell[TextData[{ "A este mismo resultado podemos llegar directamente utilizando \ MatrixPower[A,n] que c\[AAcute]lcula la potencia n-\[EAcute]sima de una \ matriz A. ", StyleBox["No vale escribir", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ RowBox[{" ", SuperscriptBox["A", "n"]}], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox[" (es decir poner n como exponente de A)", FontColor->RGBColor[0, 0, 1]], " ", StyleBox["pues ", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ FormBox[ SuperscriptBox["A", "n"], TraditionalForm]], FontColor->RGBColor[0, 0, 1]], StyleBox[" = A x A x A que es distinto A . A . 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descomponiendolo en cuatro determinantes de orden 3, \ desarrollandolo por los elementos de la segunda fila (observese que es \ conveniente elegir filas con el mayor numero de ceros)\ \>", "Text"], Cell[BoxData[ RowBox[{ RowBox[{"(", GridBox[{ {"3", "2", "1", RowBox[{"-", "1"}]}, {"1", "0", RowBox[{"-", "3"}], "2"}, {"3", "2", "0", "5"}, {"2", RowBox[{"-", "1"}], "2", "4"} }], ")"}], "=", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], RowBox[{"2", "+", "1"}]], " ", "1", RowBox[{"(", GridBox[{ {"2", "1", RowBox[{"-", "1"}]}, {"2", "0", "5"}, { RowBox[{"-", "1"}], "2", "4"} }], ")"}]}], "+", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], RowBox[{"2", "+", "2"}]], "0", RowBox[{"(", GridBox[{ {"3", "1", RowBox[{"-", "1"}]}, {"3", "0", "5"}, {"2", "2", "4"} }], ")"}]}], "+", "\[IndentingNewLine]", RowBox[{ RowBox[{"+", SuperscriptBox[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], RowBox[{"2", "+", "3"}]]}], RowBox[{"(", RowBox[{"-", "3"}], 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Para girar 180\.ba multiplicar por ", Cell[BoxData[ FormBox[ RowBox[{"[", GridBox[{ { RowBox[{"-", "1"}], "0"}, {"0", RowBox[{"-", "1"}]} }], "]"}], TraditionalForm]]], ". Para girar 270\.ba (antihorario) multiplicar por ", Cell[BoxData[ FormBox[ RowBox[{"[", GridBox[{ {"0", "1"}, { RowBox[{"-", "1"}], "0"} }], "]"}], TraditionalForm]]], ". 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