(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 25063, 640] NotebookOptionsPosition[ 7231, 299] NotebookOutlinePosition[ 24003, 602] CellTagsIndexPosition[ 23960, 599] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Tarea 4\.aa: Vectores, matrices y otras cuestiones de \[AAcute]lgebra lineal\ \>", "Title", CellChangeTimes->{ 3.427806402089074*^9, 3.464433251405252*^9, {3.467635644578125*^9, 3.467635671546875*^9}}, TextAlignment->Center], Cell[CellGroupData[{ Cell[TextData[{ "Ejercicio 1\nDefinir una matriz de 3 filas y 4 columnas, en la que cada \ elemento\n ", Cell[BoxData[ SubscriptBox["c", RowBox[{"i", ",", "j"}]]]], "=", Cell[BoxData[ RowBox[{"cos", RowBox[{"(", RowBox[{ SuperscriptBox["j", 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"3", RowBox[{"-", "2"}]}, { RowBox[{"-", "4"}], "4", "2", RowBox[{"-", "3"}]} }], ")"}], MatrixForm[#]& ]]], " y B=", Cell[BoxData[ TagBox[ RowBox[{"(", GridBox[{ {"1", RowBox[{"-", "2"}]}, { RowBox[{"-", "4"}], "3"}, {"4", RowBox[{"-", "4"}]}, { RowBox[{"-", "5"}], RowBox[{"-", "3"}]} }], ")"}], MatrixForm[#]& ]]], ", calcular A.B y B.A." }], "Subsection", CellChangeTimes->{{3.427541387265374*^9, 3.427541389995976*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"matriza", "=", RowBox[{"(", GridBox[{ { RowBox[{"-", "1"}], RowBox[{"-", "5"}], RowBox[{"-", "5"}], RowBox[{"-", "4"}]}, { RowBox[{"-", "3"}], "5", "3", RowBox[{"-", "2"}]}, { RowBox[{"-", "4"}], "4", "2", RowBox[{"-", "3"}]} }], ")"}]}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"matrizb", "=", RowBox[{"(", GridBox[{ {"1", RowBox[{"-", "2"}]}, { RowBox[{"-", "4"}], "3"}, {"4", RowBox[{"-", "4"}]}, { RowBox[{"-", "5"}], RowBox[{"-", "3"}]} }], ")"}]}], ";"}]], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Ejercicio 4 Resolver el sistema de ecuaciones: x- y+z=1 -x+5y+z=1 x+y+3z=0\ \>", "Subsection", CellChangeTimes->{{3.4275413980745707`*^9, 3.427541399843322*^9}, { 3.464433526186502*^9, 3.4644335586083765`*^9}}], Cell[BoxData[""], "Input", CellChangeTimes->{{3.4644335664208765`*^9, 3.4644335677958765`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Ejercicio 5 Resolver el sistema de ecuaciones y verificar la soluci\[OAcute]n obtenida x+2y=3 y+z=1 -2x-4y+z=1\ \>", "Subsection", CellChangeTimes->{{3.427541408049371*^9, 3.4275414110093613`*^9}, { 3.4644336516083765`*^9, 3.4644336966083765`*^9}}], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.4644337314521265`*^9}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Ejercicio 6 Resolver el sistema y verificar la soluci\[OAcute]n 6x-2y+2z+4t=10 12x-8y+6z+10t=20 3x-13y+9z+3t=2 -6x+4y+z-18t=-19\ \>", "Subsection", CellChangeTimes->{{3.4275406973965816`*^9, 3.4275408987379713`*^9}, { 3.427541417787428*^9, 3.427541419407279*^9}, 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"\nHallar los valores y vectores propios de A, de forma exacta y aproximada.\ \n" }], "Subsection", CellChangeTimes->{{3.427541440354751*^9, 3.427541443249403*^9}, { 3.4278064399079027`*^9, 3.427806440619816*^9}, {3.464434224999002*^9, 3.464434304186502*^9}}, TextAlignment->Left, TextJustification->1], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.4286683833125*^9}] }, Open ]] }, Open ]] }, WindowToolbars->{"RulerBar", "EditBar"}, WindowSize->{1672, 933}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, DockedCells->FEPrivate`If[ FEPrivate`SameQ[FEPrivate`$ProductIDName, "MathematicaPlayer"], FEPrivate`Join[{ Cell[ BoxData[ GraphicsBox[ RasterBox[CompressedData[" 1:eJztXXdYFNfaz3O/f+79vudek3vTLKBIEaQpTRC7BgtqLCTWGxNjYsFookE0 NoxRY6oFuyIiWJCO9N4WWHrZpSy7VKkiBo2iy+5+Z/fsHg4zO7NLUZJ4fs/I Mztz5j3v+87u+zvnPe+Meuu3L1v/P6+99poJ+Gf+t9dek+8LBwiBIHvu/Byd ManLXMoSE+ExkQoZX+8W641rHWPUaDZZav+BZOoa6ZRVkhkftXrdrC3lg60h JuGh667nVjNkJjbd4ywfjhzbcP7iQFUiICAgIHiVkHfVO0dHL0tnDFd/XNGH 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