(* Content-type: application/mathematica *)

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

(* CreatedBy='Mathematica 7.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[      9530,        266]
NotebookOptionsPosition[      7474,        220]
NotebookOutlinePosition[      7989,        238]
CellTagsIndexPosition[      7946,        235]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["Ejercicio 1", "Subtitle",
 CellChangeTimes->{{3.558873232104956*^9, 3.5588732348351126`*^9}, {
  3.6167508966775894`*^9, 
  3.616750897808654*^9}},ExpressionUUID->"6b84a210-2e5b-4464-9130-\
5b586532bccd"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"TT", "=", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"3", ",", 
      RowBox[{"-", "10"}], ",", "0"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "10"}], ",", "0", ",", "30"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"0", ",", "30", ",", 
      RowBox[{"-", "27"}]}], "}"}]}], "}"}]}]], "Input",
 CellChangeTimes->{{3.5588732546642466`*^9, 3.5588732854600077`*^9}, 
   3.5588733265683594`*^9, {3.8225610172877493`*^9, 3.8225610563051395`*^9}},
 CellLabel->"In[1]:=",ExpressionUUID->"376a7df0-9df3-42bc-beda-114f9f1e9e76"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"3", ",", 
     RowBox[{"-", "10"}], ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "10"}], ",", "0", ",", "30"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "30", ",", 
     RowBox[{"-", "27"}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.558873286949093*^9, 3.558873327857433*^9, 3.6167509108854017`*^9, 
   3.82255897076429*^9, 3.8225592315124097`*^9, 3.822561057829962*^9, {
   3.8225611401682596`*^9, 3.8225611559066315`*^9}},
 CellLabel->"Out[1]=",ExpressionUUID->"7d77859a-b46b-42ed-be86-7f7c36128294"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"CharacteristicPolynomial", "[", 
  RowBox[{"TT", ",", "x"}], "]"}]], "Input",
 CellChangeTimes->{{3.6167509275293536`*^9, 3.61675095560896*^9}, {
  3.6167510076849384`*^9, 3.6167510123842072`*^9}},
 CellLabel->"In[2]:=",ExpressionUUID->"d9f52117-45da-4186-9bdc-c2446166b575"],

Cell[BoxData[
 RowBox[{
  RowBox[{"1081", " ", "x"}], "-", 
  RowBox[{"24", " ", 
   SuperscriptBox["x", "2"]}], "-", 
  SuperscriptBox["x", "3"]}]], "Output",
 CellChangeTimes->{
  3.6167509570290413`*^9, 3.6167510138072886`*^9, 3.8225589747075357`*^9, 
   3.822559234882031*^9, 3.822561071359032*^9, {3.8225611402485933`*^9, 
   3.822561158613087*^9}},
 CellLabel->"Out[2]=",ExpressionUUID->"0e602ea4-0316-4711-95e8-a3e57716bcda"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"N", "[", 
  RowBox[{"Eigenvalues", "[", "TT", "]"}], "]"}]], "Input",
 CellChangeTimes->{{3.558873290758311*^9, 3.5588733134966116`*^9}},
 CellLabel->"In[3]:=",ExpressionUUID->"5722929e-982f-4199-b4af-a180b6978721"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"-", "47.`"}], ",", "23.`", ",", "0.`"}], "}"}]], "Output",
 CellChangeTimes->{{3.5588732995288124`*^9, 3.5588733311376204`*^9}, 
   3.8225589771702337`*^9, 3.8225592369616017`*^9, 3.8225610761121855`*^9, {
   3.8225611402501016`*^9, 3.8225611587893496`*^9}},
 CellLabel->"Out[3]=",ExpressionUUID->"031401fe-cd6c-46c3-a258-4a5c11ac09a7"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"v", "=", 
  RowBox[{"Eigenvectors", "[", "TT", "]"}]}]], "Input",
 CellChangeTimes->{{3.5588756002494063`*^9, 3.5588756135721684`*^9}, {
  3.822559263781192*^9, 3.822559266586707*^9}, {3.8225594047311745`*^9, 
  3.8225594069020944`*^9}},
 CellLabel->"In[4]:=",ExpressionUUID->"6640be87-a504-45c8-b195-c32ab47fcd16"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "2"}], ",", 
     RowBox[{"-", "10"}], ",", "15"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "5"}], ",", "10", ",", "6"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"30", ",", "9", ",", "10"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.5588756176704025`*^9, 3.822558994496473*^9, 3.82255926918386*^9, {
   3.8225611133888187`*^9, 3.8225611588487267`*^9}},
 CellLabel->"Out[4]=",ExpressionUUID->"cf5e724a-c302-4481-aff9-e0d94975f31e"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"vn1", "=", 
  RowBox[{"N", "[", 
   RowBox[{
    RowBox[{"v", "[", 
     RowBox[{"[", "1", "]"}], "]"}], "/", 
    RowBox[{"Norm", "[", 
     RowBox[{"v", "[", 
      RowBox[{"[", "1", "]"}], "]"}], "]"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.5588763655531793`*^9, 3.558876390876628*^9}, {
   3.822559690801545*^9, 3.8225596941166134`*^9}, 3.8225605366233244`*^9, {
   3.822560636401231*^9, 3.8225606413858147`*^9}},
 CellLabel->"In[5]:=",ExpressionUUID->"a3b99350-cb39-43db-b225-ba8686134c23"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"-", "0.11026356928399425`"}], ",", 
   RowBox[{"-", "0.5513178464199713`"}], ",", "0.8269767696299569`"}], 
  "}"}]], "Output",
 CellChangeTimes->{{3.5588763792069597`*^9, 3.558876391757678*^9}, 
   3.5588765242642565`*^9, 3.558876642982047*^9, 3.5588777856164017`*^9, 
   3.8225590222246017`*^9, 3.822559272988114*^9, 3.8225596960042896`*^9, 
   3.8225604570607905`*^9, 3.822560644086085*^9, {3.822561126346507*^9, 
   3.822561158904699*^9}},
 CellLabel->"Out[5]=",ExpressionUUID->"48a4d6d3-71ff-4d93-a737-ba9535d8c29f"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"vn2", "=", 
  RowBox[{"N", "[", 
   RowBox[{
    RowBox[{"v", "[", 
     RowBox[{"[", "2", "]"}], "]"}], "/", 
    RowBox[{"Norm", "[", 
     RowBox[{"v", "[", 
      RowBox[{"[", "2", "]"}], "]"}], "]"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.5588763655531793`*^9, 3.558876390876628*^9}, {
  3.822559690801545*^9, 3.822559731359974*^9}, {3.8225606049395723`*^9, 
  3.8225606115085773`*^9}},
 CellLabel->"In[6]:=",ExpressionUUID->"9f34ee05-ba59-4912-8d24-474e8d9aafa8"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"-", "0.39405520311955033`"}], ",", "0.7881104062391007`", ",", 
   "0.47286624374346037`"}], "}"}]], "Output",
 CellChangeTimes->{{3.5588763792069597`*^9, 3.558876391757678*^9}, 
   3.5588765242642565`*^9, 3.558876642982047*^9, 3.5588777856164017`*^9, 
   3.8225590222246017`*^9, 3.822559272988114*^9, 3.8225596960042896`*^9, 
   3.8225604751904297`*^9, 3.8225606147510123`*^9, {3.8225611276707335`*^9, 
   3.822561158961568*^9}},
 CellLabel->"Out[6]=",ExpressionUUID->"51cb3d46-04d0-48ab-8d98-1f0922371fef"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"vn3", "=", 
  RowBox[{"N", "[", 
   RowBox[{
    RowBox[{"v", "[", 
     RowBox[{"[", "3", "]"}], "]"}], "/", 
    RowBox[{"Norm", "[", 
     RowBox[{"v", "[", 
      RowBox[{"[", "3", "]"}], "]"}], "]"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.82256049150589*^9, 3.8225605105878253`*^9}, {
  3.8225606738753223`*^9, 3.8225606798884506`*^9}},
 CellLabel->"In[7]:=",ExpressionUUID->"7455e211-6153-4ef3-9b83-d3257f7b169b"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "0.9124485970087103`", ",", "0.2737345791026131`", ",", 
   "0.30414953233623676`"}], "}"}]], "Output",
 CellChangeTimes->{
  3.8225605117805805`*^9, 3.822560681350879*^9, {3.822561128879904*^9, 
   3.822561159009447*^9}},
 CellLabel->"Out[7]=",ExpressionUUID->"7d4ed859-f8bd-44c2-8460-ca3c1f32d649"]
}, Open  ]]
}, Open  ]]
},
WindowSize->{784, 475},
WindowMargins->{{0, Automatic}, {Automatic, 16}},
PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> True}},
TaggingRules->{"TryRealOnly" -> False},
FrontEndVersion->"12.1 for Microsoft Windows (64-bit) (March 14, 2020)",
StyleDefinitions->"Default.nb",
ExpressionUUID->"93a08944-088e-4b54-80ff-f5502c097463"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[567, 22, 210, 4, 50, "Subtitle",ExpressionUUID->"6b84a210-2e5b-4464-9130-5b586532bccd"],
Cell[CellGroupData[{
Cell[802, 30, 587, 15, 28, "Input",ExpressionUUID->"376a7df0-9df3-42bc-beda-114f9f1e9e76"],
Cell[1392, 47, 622, 16, 28, "Output",ExpressionUUID->"7d77859a-b46b-42ed-be86-7f7c36128294"]
}, Open  ]],
Cell[CellGroupData[{
Cell[2051, 68, 299, 5, 28, "Input",ExpressionUUID->"d9f52117-45da-4186-9bdc-c2446166b575"],
Cell[2353, 75, 432, 10, 30, "Output",ExpressionUUID->"0e602ea4-0316-4711-95e8-a3e57716bcda"]
}, Open  ]],
Cell[CellGroupData[{
Cell[2822, 90, 239, 4, 28, "Input",ExpressionUUID->"5722929e-982f-4199-b4af-a180b6978721"],
Cell[3064, 96, 388, 7, 28, "Output",ExpressionUUID->"031401fe-cd6c-46c3-a258-4a5c11ac09a7"]
}, Open  ]],
Cell[CellGroupData[{
Cell[3489, 108, 339, 6, 28, "Input",ExpressionUUID->"6640be87-a504-45c8-b195-c32ab47fcd16"],
Cell[3831, 116, 550, 15, 28, "Output",ExpressionUUID->"cf5e724a-c302-4481-aff9-e0d94975f31e"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4418, 136, 524, 12, 28, "Input",ExpressionUUID->"a3b99350-cb39-43db-b225-ba8686134c23"],
Cell[4945, 150, 573, 11, 28, "Output",ExpressionUUID->"48a4d6d3-71ff-4d93-a737-ba9535d8c29f"]
}, Open  ]],
Cell[CellGroupData[{
Cell[5555, 166, 498, 12, 28, "Input",ExpressionUUID->"9f34ee05-ba59-4912-8d24-474e8d9aafa8"],
Cell[6056, 180, 560, 10, 28, "Output",ExpressionUUID->"51cb3d46-04d0-48ab-8d98-1f0922371fef"]
}, Open  ]],
Cell[CellGroupData[{
Cell[6653, 195, 448, 11, 28, "Input",ExpressionUUID->"7455e211-6153-4ef3-9b83-d3257f7b169b"],
Cell[7104, 208, 342, 8, 53, "Output",ExpressionUUID->"7d4ed859-f8bd-44c2-8460-ca3c1f32d649"]
}, Open  ]]
}, Open  ]]
}
]
*)