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

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

(* CreatedBy='Mathematica 8.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       157,          7]
NotebookDataLength[     99088,       2896]
NotebookOptionsPosition[     92294,       2668]
NotebookOutlinePosition[     92637,       2683]
CellTagsIndexPosition[     92594,       2680]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", 
  StyleBox[
   RowBox[{
   "\:041c\:0410\:0422\:0420\:0418\:0426\:0418", " ", "\:0418", " ", 
    "\:041e\:041f\:0415\:0420\:0410\:0426\:0418\:0418", " ", "\:0421", " ", 
    "\:041c\:0410\:0422\:0420\:0418\:0426\:0418"}],
   FontFamily->"Courier New",
   FontSize->20]}]], "Input",
 CellChangeTimes->{{3.65863800931742*^9, 3.658638030699643*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"{", 
   RowBox[{"a", ",", "b", ",", "c"}], "}"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.624074824112796*^9, 3.6240748284964037`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"a", ",", "b", ",", "c"}], "}"}]], "Output",
 CellChangeTimes->{3.6240819550813556`*^9, 3.658633546977189*^9, 
  3.6586381055739255`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"m", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"a", ",", "b"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"c", ",", "d"}], "}"}]}], "}"}]}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240748809163017`*^9, 3.624074910525154*^9}, {
   3.624074948647302*^9, 3.6240749497237043`*^9}, 3.6240750182556243`*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"a", ",", "b"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"c", ",", "d"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.62408199735023*^9, 3.65863355102242*^9, 
  3.658638114947462*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"m", "//", " ", "MatrixForm"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240750364608564`*^9, 3.6240750482086773`*^9}}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"a", "b"},
     {"c", "d"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "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",
 CellChangeTimes->{3.6240820046978436`*^9, 3.6586335576317983`*^9, 
  3.65863812574708*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"m", "[", 
   RowBox[{"[", "1", "]"}], "]"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240749719381433`*^9, 3.624074975307749*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"a", ",", "b"}], "}"}]], "Output",
 CellChangeTimes->{3.6240820275674834`*^9, 3.6586335601759434`*^9, 
  3.658638133852543*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"m", "[", 
   RowBox[{"[", 
    RowBox[{"1", ",", "2"}], "]"}], "]"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240751136159925`*^9, 3.6240751201836042`*^9}}],

Cell[BoxData["b"], "Output",
 CellChangeTimes->{3.6240820492515216`*^9, 3.6586335631221123`*^9, 
  3.658638156051813*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"v", "=", 
   RowBox[{"{", 
    RowBox[{"x", ",", "y"}], "}"}]}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.624075227410593*^9, 3.624075235226207*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"x", ",", "y"}], "}"}]], "Output",
 CellChangeTimes->{3.6240820835257816`*^9, 3.6586335671633434`*^9, 
  3.6586381701246176`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{
   RowBox[{"p", " ", "v"}], "+", "q"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240752526982374`*^9, 3.624075257659046*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"q", "+", 
    RowBox[{"p", " ", "x"}]}], ",", 
   RowBox[{"q", "+", 
    RowBox[{"p", " ", "y"}]}]}], "}"}]], "Output",
 CellChangeTimes->{3.65863820705873*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"v", "+", 
   RowBox[{"{", 
    RowBox[{"xp", ",", "yp"}], "}"}], "+", 
   RowBox[{"{", 
    RowBox[{"xpp", ",", "ypp"}], "}"}]}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.624075330902175*^9, 3.6240753517136116`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"x", "+", "xp", "+", "xpp"}], ",", 
   RowBox[{"y", "+", "yp", "+", "ypp"}]}], "}"}]], "Output",
 CellChangeTimes->{3.6240821767827454`*^9, 3.6586335826412287`*^9, 
  3.6586382149781833`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", ",", "y"}], "}"}], ".", 
   RowBox[{"{", 
    RowBox[{"xp", ",", "yp"}], "}"}]}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240754313215513`*^9, 3.6240754467967787`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"x", " ", "xp"}], "+", 
  RowBox[{"y", " ", "yp"}]}]], "Output",
 CellChangeTimes->{3.624082208232401*^9, 3.6586335906746883`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", ",", "y"}], "}"}], 
   RowBox[{"{", 
    RowBox[{"xp", ",", "yp"}], "}"}]}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{3.624075479479836*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"x", " ", "xp"}], ",", 
   RowBox[{"y", " ", "yp"}]}], "}"}]], "Output",
 CellChangeTimes->{3.624082223411227*^9, 3.6586335938878717`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"m", ".", "v"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.624075542350747*^9, 3.624075544690751*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{
    RowBox[{"a", " ", "x"}], "+", 
    RowBox[{"b", " ", "y"}]}], ",", 
   RowBox[{
    RowBox[{"c", " ", "x"}], "+", 
    RowBox[{"d", " ", "y"}]}]}], "}"}]], "Output",
 CellChangeTimes->{3.624082332502219*^9, 3.6586382308440905`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"v", ".", "m"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240756084646626`*^9, 3.624075610976267*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{
    RowBox[{"a", " ", "x"}], "+", 
    RowBox[{"c", " ", "y"}]}], ",", 
   RowBox[{
    RowBox[{"b", " ", "x"}], "+", 
    RowBox[{"d", " ", "y"}]}]}], "}"}]], "Output",
 CellChangeTimes->{3.6240823795207014`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{
   RowBox[{"m", ".", "m"}], " ", "//", "MatrixForm"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240756942648134`*^9, 3.624075724015066*^9}}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {
      RowBox[{
       SuperscriptBox["a", "2"], "+", 
       RowBox[{"b", " ", "c"}]}], 
      RowBox[{
       RowBox[{"a", " ", "b"}], "+", 
       RowBox[{"b", " ", "d"}]}]},
     {
      RowBox[{
       RowBox[{"a", " ", "c"}], "+", 
       RowBox[{"c", " ", "d"}]}], 
      RowBox[{
       RowBox[{"b", " ", "c"}], "+", 
       SuperscriptBox["d", "2"]}]}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "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",
 CellChangeTimes->{
  3.6240824238871794`*^9, {3.6586335995401955`*^9, 3.6586336125889416`*^9}, 
   3.6586382409676695`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"v", ".", "m", ".", "v"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.624075786633576*^9, 3.624075790190382*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"x", " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"a", " ", "x"}], "+", 
     RowBox[{"c", " ", "y"}]}], ")"}]}], "+", 
  RowBox[{"y", " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"b", " ", "x"}], "+", 
     RowBox[{"d", " ", "y"}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{3.6240824619668465`*^9, 3.658638380357642*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"Dot", "[", 
   RowBox[{"v", ",", "m", ",", "v"}], "]"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240758697505217`*^9, 3.6240758768953342`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"x", " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"a", " ", "x"}], "+", 
     RowBox[{"c", " ", "y"}]}], ")"}]}], "+", 
  RowBox[{"y", " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"b", " ", "x"}], "+", 
     RowBox[{"d", " ", "y"}]}], ")"}]}]}]], "Output",
 CellChangeTimes->{3.6240825013725157`*^9, 3.6586384246351748`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"Det", "[", "m", "]"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240759640868874`*^9, 3.624075967737294*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"-", "b"}], " ", "c"}], "+", 
  RowBox[{"a", " ", "d"}]}]], "Output",
 CellChangeTimes->{3.624082590791873*^9, 3.658638430887532*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{
   RowBox[{"Transpose", "[", "m", "]"}], "//", " ", "MatrixForm"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240760295300026`*^9, 3.6240760612292585`*^9}}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"a", "c"},
     {"b", "d"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "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",
 CellChangeTimes->{3.6240826557035866`*^9, 3.6586336455638275`*^9, 
  3.6586384428522167`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"n", "=", 
   RowBox[{"Inverse", "[", "m", "]"}]}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.624076115236553*^9, 3.624076122132766*^9}, {
  3.6240761723960533`*^9, 3.6240761733476553`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     FractionBox["d", 
      RowBox[{
       RowBox[{
        RowBox[{"-", "b"}], " ", "c"}], "+", 
       RowBox[{"a", " ", "d"}]}]], ",", 
     RowBox[{"-", 
      FractionBox["b", 
       RowBox[{
        RowBox[{
         RowBox[{"-", "b"}], " ", "c"}], "+", 
        RowBox[{"a", " ", "d"}]}]]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", 
      FractionBox["c", 
       RowBox[{
        RowBox[{
         RowBox[{"-", "b"}], " ", "c"}], "+", 
        RowBox[{"a", " ", "d"}]}]]}], ",", 
     FractionBox["a", 
      RowBox[{
       RowBox[{
        RowBox[{"-", "b"}], " ", "c"}], "+", 
       RowBox[{"a", " ", "d"}]}]]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.624082712409686*^9, 3.6586336553573875`*^9, 
  3.658638448220524*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{
   RowBox[{"n", " ", ".", " ", "m"}], " ", "//", "Simplify"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240761454080067`*^9, 3.624076186858279*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"1", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "1"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.624082726340511*^9, 3.6586384636344056`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"  ", 
   RowBox[{
    RowBox[{"m", " ", ".", " ", "n"}], " ", "//", "Simplify"}]}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240762112723217`*^9, 3.624076233549161*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"1", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "1"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.624082741768938*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 StyleBox[
  RowBox[{"h3", "=", 
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"1", "/", 
      RowBox[{"(", 
       RowBox[{"i", "+", "j", "-", "1"}], ")"}]}], ",", 
     RowBox[{"{", 
      RowBox[{"i", ",", "3"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j", ",", "3"}], "}"}]}], "]"}]}],
  FontFamily->"Courier New",
  FontSize->24], "\[IndentingNewLine]", 
 StyleBox[
  RowBox[{"Det", "[", "h3", "]"}],
  FontFamily->"Courier New",
  FontSize->24]}], "Input",
 CellChangeTimes->{{3.624076596082198*^9, 3.6240766581079073`*^9}, {
  3.6240766991827793`*^9, 3.624076706764393*^9}, {3.6240767413506536`*^9, 
  3.6240767436438575`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"1", ",", 
     FractionBox["1", "2"], ",", 
     FractionBox["1", "3"]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     FractionBox["1", "2"], ",", 
     FractionBox["1", "3"], ",", 
     FractionBox["1", "4"]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     FractionBox["1", "3"], ",", 
     FractionBox["1", "4"], ",", 
     FractionBox["1", "5"]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.624082986058567*^9, 3.6586385252949324`*^9}],

Cell[BoxData[
 FractionBox["1", "2160"]], "Output",
 CellChangeTimes->{3.624082986058567*^9, 3.658638525323934*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{
   RowBox[{"Inverse", "[", "h3", "]"}], "//", "MatrixForm"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240782810181866`*^9, 3.6240783016590233`*^9}}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"9", 
      RowBox[{"-", "36"}], "30"},
     {
      RowBox[{"-", "36"}], "192", 
      RowBox[{"-", "180"}]},
     {"30", 
      RowBox[{"-", "180"}], "180"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "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",
 CellChangeTimes->{3.624083003982999*^9, 3.658638601935316*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 StyleBox[
  RowBox[{"h4", "=", 
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"1", "/", 
      RowBox[{"(", 
       RowBox[{"i", "+", "j", "-", "1"}], ")"}]}], ",", 
     RowBox[{"{", 
      RowBox[{"i", ",", "4"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j", ",", "4"}], "}"}]}], "]"}]}],
  FontFamily->"Courier New",
  FontSize->24], "\[IndentingNewLine]", 
 StyleBox[
  RowBox[{"Det", "[", "h4", "]"}],
  FontFamily->"Courier New",
  FontSize->24]}], "Input",
 CellChangeTimes->{{3.624081839406953*^9, 3.6240818479099674`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"1", ",", 
     FractionBox["1", "2"], ",", 
     FractionBox["1", "3"], ",", 
     FractionBox["1", "4"]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     FractionBox["1", "2"], ",", 
     FractionBox["1", "3"], ",", 
     FractionBox["1", "4"], ",", 
     FractionBox["1", "5"]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     FractionBox["1", "3"], ",", 
     FractionBox["1", "4"], ",", 
     FractionBox["1", "5"], ",", 
     FractionBox["1", "6"]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     FractionBox["1", "4"], ",", 
     FractionBox["1", "5"], ",", 
     FractionBox["1", "6"], ",", 
     FractionBox["1", "7"]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.624083017087022*^9, 3.6586386101697865`*^9}],

Cell[BoxData[
 FractionBox["1", "6048000"]], "Output",
 CellChangeTimes->{3.624083017087022*^9, 3.6586386101717873`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{
   RowBox[{"Inverse", "[", "h4", "]"}], "//", "MatrixForm"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240783450270996`*^9, 3.6240783454639*^9}}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"16", 
      RowBox[{"-", "120"}], "240", 
      RowBox[{"-", "140"}]},
     {
      RowBox[{"-", "120"}], "1200", 
      RowBox[{"-", "2700"}], "1680"},
     {"240", 
      RowBox[{"-", "2700"}], "6480", 
      RowBox[{"-", "4200"}]},
     {
      RowBox[{"-", "140"}], "1680", 
      RowBox[{"-", "4200"}], "2800"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "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",
 CellChangeTimes->{3.624083045573672*^9, 3.6586386181952457`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 StyleBox[
  RowBox[{"h3", ".", 
   RowBox[{"Inverse", "[", "h3", "]"}]}],
  FontFamily->"Courier New",
  FontSize->24], "\[IndentingNewLine]", 
 StyleBox[
  RowBox[{"h4", ".", 
   RowBox[{"Inverse", "[", "h4", "]"}]}],
  FontFamily->"Courier New",
  FontSize->24]}], "Input",
 CellChangeTimes->{{3.6240783576787214`*^9, 3.6240783705799446`*^9}, {
  3.6240784360844593`*^9, 3.6240784434320726`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.6240831165381966`*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"1", ",", "0", ",", "0", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "1", ",", "0", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "1", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "0", ",", "1"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.6240831165537963`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 StyleBox[
  RowBox[{"r", "=", 
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"i", "+", "j", "+", "1"}], ",", 
     RowBox[{"{", 
      RowBox[{"i", ",", "3"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j", ",", "3"}], "}"}]}], "]"}]}],
  FontFamily->"Courier New",
  FontSize->24], "\[IndentingNewLine]", 
 StyleBox[
  RowBox[{"Eigenvalues", "[", "r", "]"}],
  FontFamily->"Courier New",
  FontSize->24], "\[IndentingNewLine]", 
 StyleBox[
  RowBox[{"Eigenvectors", "[", "r", "]"}],
  FontFamily->"Courier New",
  FontSize->24]}], "Input",
 CellChangeTimes->{{3.6240785357374344`*^9, 3.624078558794275*^9}, {
  3.624078629306399*^9, 3.62407865273764*^9}, {3.624078707322136*^9, 
  3.6240787085233383`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"3", ",", "4", ",", "5"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"4", ",", "5", ",", "6"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"5", ",", "6", ",", "7"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.6240832692000647`*^9, 3.6586387959044104`*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{"15", "+", 
      SqrtBox["249"]}], ")"}]}], ",", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{"15", "-", 
      SqrtBox["249"]}], ")"}]}], ",", "0"}], "}"}]], "Output",
 CellChangeTimes->{3.6240832692000647`*^9, 3.6586387959454126`*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       FractionBox["5", "4"]}], "+", 
      RowBox[{
       FractionBox["1", "16"], " ", 
       RowBox[{"(", 
        RowBox[{"15", "+", 
         SqrtBox["249"]}], ")"}]}]}], ",", 
     RowBox[{
      RowBox[{"-", 
       FractionBox["1", "8"]}], "+", 
      RowBox[{
       FractionBox["1", "32"], " ", 
       RowBox[{"(", 
        RowBox[{"15", "+", 
         SqrtBox["249"]}], ")"}]}]}], ",", "1"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{"-", 
       FractionBox["5", "4"]}], "+", 
      RowBox[{
       FractionBox["1", "16"], " ", 
       RowBox[{"(", 
        RowBox[{"15", "-", 
         SqrtBox["249"]}], ")"}]}]}], ",", 
     RowBox[{
      RowBox[{"-", 
       FractionBox["1", "8"]}], "+", 
      RowBox[{
       FractionBox["1", "32"], " ", 
       RowBox[{"(", 
        RowBox[{"15", "-", 
         SqrtBox["249"]}], ")"}]}]}], ",", "1"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1", ",", 
     RowBox[{"-", "2"}], ",", "1"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.6240832692000647`*^9, 3.658638796058419*^9}]
}, Open  ]],

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.6240788437131753`*^9, 3.624078852714391*^9}, 
   3.6240817768297334`*^9}],

Cell[CellGroupData[{

Cell[BoxData[{
 StyleBox[
  RowBox[{"rn", "=", 
   RowBox[{"N", "[", "r", "]"}]}],
  FontFamily->"Courier New",
  FontSize->24], "\[IndentingNewLine]", 
 StyleBox[
  RowBox[{"Eigenvalues", "[", "rn", "]"}],
  FontFamily->"Courier New",
  FontSize->24], "\[IndentingNewLine]", 
 StyleBox[
  RowBox[{"Eigenvectors", "[", "rn", "]"}],
  FontFamily->"Courier New",
  FontSize->24]}], "Input",
 CellChangeTimes->{{3.624078877144034*^9, 3.624078880045639*^9}, {
  3.624081778748537*^9, 3.62408178125896*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"3.`", ",", "4.`", ",", "5.`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"4.`", ",", "5.`", ",", "6.`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"5.`", ",", "6.`", ",", "7.`"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.624083365530234*^9, 3.658638900043367*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"15.38986691902975`", ",", 
   RowBox[{"-", "0.3898669190297511`"}], ",", 
   RowBox[{"-", "1.8985108819428066`*^-15"}]}], "}"}]], "Output",
 CellChangeTimes->{3.624083365530234*^9, 3.6586389001673737`*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
    "0.45902754301480775`", ",", "0.5701734203711937`", ",", 
     "0.6813192977275799`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "0.7890672012491198`"}], ",", 
     RowBox[{"-", "0.09075022884570527`"}], ",", "0.6075667435577207`"}], 
    "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.40824829046386696`", ",", 
     RowBox[{"-", "0.8164965809277254`"}], ",", "0.4082482904638599`"}], 
    "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.624083365530234*^9, 3.6586389002143764`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"mm", "=", 
   RowBox[{"Array", "[", 
    RowBox[{"a", ",", 
     RowBox[{"{", 
      RowBox[{"3", ",", "3"}], "}"}]}], "]"}]}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240791403476963`*^9, 3.62407915377932*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"a", "[", 
      RowBox[{"1", ",", "1"}], "]"}], ",", 
     RowBox[{"a", "[", 
      RowBox[{"1", ",", "2"}], "]"}], ",", 
     RowBox[{"a", "[", 
      RowBox[{"1", ",", "3"}], "]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"a", "[", 
      RowBox[{"2", ",", "1"}], "]"}], ",", 
     RowBox[{"a", "[", 
      RowBox[{"2", ",", "2"}], "]"}], ",", 
     RowBox[{"a", "[", 
      RowBox[{"2", ",", "3"}], "]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"a", "[", 
      RowBox[{"3", ",", "1"}], "]"}], ",", 
     RowBox[{"a", "[", 
      RowBox[{"3", ",", "2"}], "]"}], ",", 
     RowBox[{"a", "[", 
      RowBox[{"3", ",", "3"}], "]"}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.624083439318363*^9, 3.6586389635930014`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"Minors", "[", 
   RowBox[{"mm", ",", "2"}], "]"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240792638843136`*^9, 3.6240792725111284`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"a", "[", 
         RowBox[{"1", ",", "2"}], "]"}]}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"2", ",", "1"}], "]"}]}], "+", 
      RowBox[{
       RowBox[{"a", "[", 
        RowBox[{"1", ",", "1"}], "]"}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"2", ",", "2"}], "]"}]}]}], ",", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"a", "[", 
         RowBox[{"1", ",", "3"}], "]"}]}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"2", ",", "1"}], "]"}]}], "+", 
      RowBox[{
       RowBox[{"a", "[", 
        RowBox[{"1", ",", "1"}], "]"}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"2", ",", "3"}], "]"}]}]}], ",", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"a", "[", 
         RowBox[{"1", ",", "3"}], "]"}]}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"2", ",", "2"}], "]"}]}], "+", 
      RowBox[{
       RowBox[{"a", "[", 
        RowBox[{"1", ",", "2"}], "]"}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"2", ",", "3"}], "]"}]}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"a", "[", 
         RowBox[{"1", ",", "2"}], "]"}]}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"3", ",", "1"}], "]"}]}], "+", 
      RowBox[{
       RowBox[{"a", "[", 
        RowBox[{"1", ",", "1"}], "]"}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"3", ",", "2"}], "]"}]}]}], ",", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"a", "[", 
         RowBox[{"1", ",", "3"}], "]"}]}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"3", ",", "1"}], "]"}]}], "+", 
      RowBox[{
       RowBox[{"a", "[", 
        RowBox[{"1", ",", "1"}], "]"}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"3", ",", "3"}], "]"}]}]}], ",", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"a", "[", 
         RowBox[{"1", ",", "3"}], "]"}]}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"3", ",", "2"}], "]"}]}], "+", 
      RowBox[{
       RowBox[{"a", "[", 
        RowBox[{"1", ",", "2"}], "]"}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"3", ",", "3"}], "]"}]}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"a", "[", 
         RowBox[{"2", ",", "2"}], "]"}]}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"3", ",", "1"}], "]"}]}], "+", 
      RowBox[{
       RowBox[{"a", "[", 
        RowBox[{"2", ",", "1"}], "]"}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"3", ",", "2"}], "]"}]}]}], ",", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"a", "[", 
         RowBox[{"2", ",", "3"}], "]"}]}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"3", ",", "1"}], "]"}]}], "+", 
      RowBox[{
       RowBox[{"a", "[", 
        RowBox[{"2", ",", "1"}], "]"}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"3", ",", "3"}], "]"}]}]}], ",", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"a", "[", 
         RowBox[{"2", ",", "3"}], "]"}]}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"3", ",", "2"}], "]"}]}], "+", 
      RowBox[{
       RowBox[{"a", "[", 
        RowBox[{"2", ",", "2"}], "]"}], " ", 
       RowBox[{"a", "[", 
        RowBox[{"3", ",", "3"}], "]"}]}]}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.6240835509375596`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"tr", "=", 
   RowBox[{"Sum", "[", 
    RowBox[{
     RowBox[{"m", "[", 
      RowBox[{"[", 
       RowBox[{"i", ",", "i"}], "]"}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"i", ",", "2"}], "}"}]}], "]"}]}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.624079437325418*^9, 3.624079462925063*^9}}],

Cell[BoxData[
 RowBox[{"a", "+", "d"}]], "Output",
 CellChangeTimes->{3.6240836902926044`*^9, 3.6586391391970453`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"Tr", "[", "m", "]"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240797654719944`*^9, 3.6240797695124016`*^9}}],

Cell[BoxData[
 RowBox[{"a", "+", "d"}]], "Output",
 CellChangeTimes->{3.6240836965014153`*^9, 3.6586391529608326`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"MatrixPower", "[", 
   RowBox[{"m", ",", "3"}], "]"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.624079640890176*^9, 3.624079651810195*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{"a", " ", 
       RowBox[{"(", 
        RowBox[{
         SuperscriptBox["a", "2"], "+", 
         RowBox[{"b", " ", "c"}]}], ")"}]}], "+", 
      RowBox[{"b", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a", " ", "c"}], "+", 
         RowBox[{"c", " ", "d"}]}], ")"}]}]}], ",", 
     RowBox[{
      RowBox[{"a", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a", " ", "b"}], "+", 
         RowBox[{"b", " ", "d"}]}], ")"}]}], "+", 
      RowBox[{"b", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"b", " ", "c"}], "+", 
         SuperscriptBox["d", "2"]}], ")"}]}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{"c", " ", 
       RowBox[{"(", 
        RowBox[{
         SuperscriptBox["a", "2"], "+", 
         RowBox[{"b", " ", "c"}]}], ")"}]}], "+", 
      RowBox[{"d", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a", " ", "c"}], "+", 
         RowBox[{"c", " ", "d"}]}], ")"}]}]}], ",", 
     RowBox[{
      RowBox[{"c", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"a", " ", "b"}], "+", 
         RowBox[{"b", " ", "d"}]}], ")"}]}], "+", 
      RowBox[{"d", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"b", " ", "c"}], "+", 
         SuperscriptBox["d", "2"]}], ")"}]}]}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.6240837467647038`*^9, 3.658639171513894*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"m", "^", "3"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240837566083207`*^9, 3.6240837588391247`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     SuperscriptBox["a", "3"], ",", 
     SuperscriptBox["b", "3"]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     SuperscriptBox["c", "3"], ",", 
     SuperscriptBox["d", "3"]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.624083769197543*^9, 3.6586392206197023`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"mmm", "=", 
   RowBox[{"(", GridBox[{
      {"0.4", "0.6"},
      {"0.525", "0.475"}
     }], ")"}]}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.624079847871339*^9, 3.624079898087827*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"0.4`", ",", "0.6`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.525`", ",", "0.475`"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.6240838254512415`*^9, 3.6586392320523567`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"MatrixPower", "[", 
   RowBox[{"mmm", ",", "3"}], "]"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.624079914280656*^9, 3.6240799146862564`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"0.46562499999999996`", ",", "0.534375`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.467578125`", ",", "0.5324218749999999`"}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.624083849538684*^9, 3.6586392359195776`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"mmm", ".", "mmm", ".", "mmm"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240799238590727`*^9, 3.624079927306679*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"0.46562499999999996`", ",", "0.534375`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.46757812500000007`", ",", "0.5324218749999999`"}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.624083859351101*^9, 3.6586392450471*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"MatrixExp", "[", "mmm", "]"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240816604657035`*^9, 3.6240816727897253`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"1.7391965346593388`", ",", "0.9790852937997064`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.8566996320747432`", ",", "1.861582196384302`"}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.624083912203994*^9, 3.6586392607809997`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"Exp", "[", "mmm", "]"}],
  FontFamily->"Courier New",
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6240816866269493`*^9, 3.624081687640951*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"1.4918246976412703`", ",", "1.8221188003905089`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.6904588483790914`", ",", "1.608014197485783`"}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.6240839219228115`*^9, 3.658639319300347*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"A", "=", 
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"i", " ", "j", " ", 
      RowBox[{"Min", "[", 
       RowBox[{"i", ",", "j"}], "]"}]}], ",", 
     RowBox[{"{", 
      RowBox[{"i", ",", "6"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"j", ",", "6"}], "}"}]}], "]"}]}],
  FontSize->18]], "Input",
 CellChangeTimes->{{3.6586344041322155`*^9, 3.658634438504181*^9}, {
  3.6586395106122894`*^9, 3.6586395128114147`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"1", ",", "2", ",", "3", ",", "4", ",", "5", ",", "6"}], "}"}], 
   ",", 
   RowBox[{"{", 
    RowBox[{"2", ",", "8", ",", "12", ",", "16", ",", "20", ",", "24"}], 
    "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"3", ",", "12", ",", "27", ",", "36", ",", "45", ",", "54"}], 
    "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"4", ",", "16", ",", "36", ",", "64", ",", "80", ",", "96"}], 
    "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"5", ",", "20", ",", "45", ",", "80", ",", "125", ",", "150"}], 
    "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"6", ",", "24", ",", "54", ",", "96", ",", "150", ",", "216"}], 
    "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.6586344400122676`*^9, 3.658635516144819*^9, 
  3.6586393588926115`*^9, 3.6586395143965054`*^9}]
}, Open  ]],

Cell[BoxData[
 StyleBox[
  RowBox[{"A", " ", "//", "MatrixForm"}],
  FontSize->18]], "Input",
 CellChangeTimes->{{3.65863444477654*^9, 3.6586344501728487`*^9}}],

Cell[BoxData[
 StyleBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {"1", "2", "3", "4", "5", "6"},
      {"2", "8", "12", "16", "20", "24"},
      {"3", "12", "27", "36", "45", "54"},
      {"4", "16", "36", "64", "80", "96"},
      {"5", "20", "45", "80", "125", "150"},
      {"6", "24", "54", "96", "150", "216"}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "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$, 
    MatrixForm[BoxForm`e$]]],
  FontSize->18]], "Input",
 CellChangeTimes->{3.6586395313714767`*^9}],

Cell[BoxData[
 StyleBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {"1", "2", "3", "4"},
      {"2", "8", "12", "16"},
      {"3", "12", "27", "36"},
      {"4", "16", "36", "64"}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "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$, 
    MatrixForm[BoxForm`e$]]],
  FontSize->18]], "Input",
 CellChangeTimes->{3.658639372096367*^9}],

Cell[BoxData[
 StyleBox[
  RowBox[{
   RowBox[{"Inverse", "[", "A", "]"}], " ", "//", "MatrixForm"}],
  FontSize->18]], "Input",
 CellChangeTimes->{{3.6586344542920847`*^9, 3.658634466410777*^9}}],

Cell[BoxData[
 StyleBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {"2", 
       RowBox[{"-", 
        FractionBox["1", "2"]}], "0", "0", "0", "0"},
      {
       RowBox[{"-", 
        FractionBox["1", "2"]}], 
       FractionBox["1", "2"], 
       RowBox[{"-", 
        FractionBox["1", "6"]}], "0", "0", "0"},
      {"0", 
       RowBox[{"-", 
        FractionBox["1", "6"]}], 
       FractionBox["2", "9"], 
       RowBox[{"-", 
        FractionBox["1", "12"]}], "0", "0"},
      {"0", "0", 
       RowBox[{"-", 
        FractionBox["1", "12"]}], 
       FractionBox["1", "8"], 
       RowBox[{"-", 
        FractionBox["1", "20"]}], "0"},
      {"0", "0", "0", 
       RowBox[{"-", 
        FractionBox["1", "20"]}], 
       FractionBox["2", "25"], 
       RowBox[{"-", 
        FractionBox["1", "30"]}]},
      {"0", "0", "0", "0", 
       RowBox[{"-", 
        FractionBox["1", "30"]}], 
       FractionBox["1", "36"]}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "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$, 
    MatrixForm[BoxForm`e$]]],
  FontSize->24]], "Input",
 CellChangeTimes->{3.658639549424509*^9}],

Cell[BoxData[
 StyleBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {"2", 
       RowBox[{"-", 
        FractionBox["1", "2"]}], "0", "0"},
      {
       RowBox[{"-", 
        FractionBox["1", "2"]}], 
       FractionBox["1", "2"], 
       RowBox[{"-", 
        FractionBox["1", "6"]}], "0"},
      {"0", 
       RowBox[{"-", 
        FractionBox["1", "6"]}], 
       FractionBox["2", "9"], 
       RowBox[{"-", 
        FractionBox["1", "12"]}]},
      {"0", "0", 
       RowBox[{"-", 
        FractionBox["1", "12"]}], 
       FractionBox["1", "16"]}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "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$, 
    MatrixForm[BoxForm`e$]]],
  FontSize->18]], "Input",
 CellChangeTimes->{3.658639396530764*^9}],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"MatrixRank", "[", "A", "]"}],
  FontSize->24]], "Input",
 CellChangeTimes->{{3.658635500898947*^9, 3.658635507618331*^9}}],

Cell[BoxData["6"], "Output",
 CellChangeTimes->{{3.658635509152419*^9, 3.658635519560014*^9}, 
   3.658639671094468*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"Det", "[", "A", "]"}],
  FontSize->24]], "Input",
 CellChangeTimes->{{3.658635525280341*^9, 3.658635528292514*^9}}],

Cell[BoxData["518400"], "Output",
 CellChangeTimes->{3.6586355292075663`*^9, 3.658639693585755*^9}]
}, Open  ]],

Cell[BoxData[
 StyleBox[
  RowBox[{"Eigenvalues", "[", "A", "]"}],
  FontSize->18]], "Input",
 CellChangeTimes->{{3.658635559103276*^9, 3.6586355846387367`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"Root", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"518400", "-", 
       RowBox[{"1531872", " ", "#1"}], "+", 
       RowBox[{"993560", " ", 
        SuperscriptBox["#1", "2"]}], "-", 
       RowBox[{"219492", " ", 
        SuperscriptBox["#1", "3"]}], "+", 
       RowBox[{"17836", " ", 
        SuperscriptBox["#1", "4"]}], "-", 
       RowBox[{"441", " ", 
        SuperscriptBox["#1", "5"]}], "+", 
       SuperscriptBox["#1", "6"]}], "&"}], ",", "6"}], "]"}], ",", 
   RowBox[{"Root", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"518400", "-", 
       RowBox[{"1531872", " ", "#1"}], "+", 
       RowBox[{"993560", " ", 
        SuperscriptBox["#1", "2"]}], "-", 
       RowBox[{"219492", " ", 
        SuperscriptBox["#1", "3"]}], "+", 
       RowBox[{"17836", " ", 
        SuperscriptBox["#1", "4"]}], "-", 
       RowBox[{"441", " ", 
        SuperscriptBox["#1", "5"]}], "+", 
       SuperscriptBox["#1", "6"]}], "&"}], ",", "5"}], "]"}], ",", 
   RowBox[{"Root", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"518400", "-", 
       RowBox[{"1531872", " ", "#1"}], "+", 
       RowBox[{"993560", " ", 
        SuperscriptBox["#1", "2"]}], "-", 
       RowBox[{"219492", " ", 
        SuperscriptBox["#1", "3"]}], "+", 
       RowBox[{"17836", " ", 
        SuperscriptBox["#1", "4"]}], "-", 
       RowBox[{"441", " ", 
        SuperscriptBox["#1", "5"]}], "+", 
       SuperscriptBox["#1", "6"]}], "&"}], ",", "4"}], "]"}], ",", 
   RowBox[{"Root", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"518400", "-", 
       RowBox[{"1531872", " ", "#1"}], "+", 
       RowBox[{"993560", " ", 
        SuperscriptBox["#1", "2"]}], "-", 
       RowBox[{"219492", " ", 
        SuperscriptBox["#1", "3"]}], "+", 
       RowBox[{"17836", " ", 
        SuperscriptBox["#1", "4"]}], "-", 
       RowBox[{"441", " ", 
        SuperscriptBox["#1", "5"]}], "+", 
       SuperscriptBox["#1", "6"]}], "&"}], ",", "3"}], "]"}], ",", 
   RowBox[{"Root", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"518400", "-", 
       RowBox[{"1531872", " ", "#1"}], "+", 
       RowBox[{"993560", " ", 
        SuperscriptBox["#1", "2"]}], "-", 
       RowBox[{"219492", " ", 
        SuperscriptBox["#1", "3"]}], "+", 
       RowBox[{"17836", " ", 
        SuperscriptBox["#1", "4"]}], "-", 
       RowBox[{"441", " ", 
        SuperscriptBox["#1", "5"]}], "+", 
       SuperscriptBox["#1", "6"]}], "&"}], ",", "2"}], "]"}], ",", 
   RowBox[{"Root", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"518400", "-", 
       RowBox[{"1531872", " ", "#1"}], "+", 
       RowBox[{"993560", " ", 
        SuperscriptBox["#1", "2"]}], "-", 
       RowBox[{"219492", " ", 
        SuperscriptBox["#1", "3"]}], "+", 
       RowBox[{"17836", " ", 
        SuperscriptBox["#1", "4"]}], "-", 
       RowBox[{"441", " ", 
        SuperscriptBox["#1", "5"]}], "+", 
       SuperscriptBox["#1", "6"]}], "&"}], ",", "1"}], "]"}]}], "}"}]], \
"Input",
 CellChangeTimes->{3.6586398073142595`*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"Root", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"518400", "-", 
       RowBox[{"1531872", " ", "#1"}], "+", 
       RowBox[{"993560", " ", 
        SuperscriptBox["#1", "2"]}], "-", 
       RowBox[{"219492", " ", 
        SuperscriptBox["#1", "3"]}], "+", 
       RowBox[{"17836", " ", 
        SuperscriptBox["#1", "4"]}], "-", 
       RowBox[{"441", " ", 
        SuperscriptBox["#1", "5"]}], "+", 
       SuperscriptBox["#1", "6"]}], "&"}], ",", "6"}], "]"}], ",", 
   RowBox[{"Root", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"518400", "-", 
       RowBox[{"1531872", " ", "#1"}], "+", 
       RowBox[{"993560", " ", 
        SuperscriptBox["#1", "2"]}], "-", 
       RowBox[{"219492", " ", 
        SuperscriptBox["#1", "3"]}], "+", 
       RowBox[{"17836", " ", 
        SuperscriptBox["#1", "4"]}], "-", 
       RowBox[{"441", " ", 
        SuperscriptBox["#1", "5"]}], "+", 
       SuperscriptBox["#1", "6"]}], "&"}], ",", "5"}], "]"}], ",", 
   RowBox[{"Root", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"518400", "-", 
       RowBox[{"1531872", " ", "#1"}], "+", 
       RowBox[{"993560", " ", 
        SuperscriptBox["#1", "2"]}], "-", 
       RowBox[{"219492", " ", 
        SuperscriptBox["#1", "3"]}], "+", 
       RowBox[{"17836", " ", 
        SuperscriptBox["#1", "4"]}], "-", 
       RowBox[{"441", " ", 
        SuperscriptBox["#1", "5"]}], "+", 
       SuperscriptBox["#1", "6"]}], "&"}], ",", "4"}], "]"}], ",", 
   RowBox[{"Root", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"518400", "-", 
       RowBox[{"1531872", " ", "#1"}], "+", 
       RowBox[{"993560", " ", 
        SuperscriptBox["#1", "2"]}], "-", 
       RowBox[{"219492", " ", 
        SuperscriptBox["#1", "3"]}], "+", 
       RowBox[{"17836", " ", 
        SuperscriptBox["#1", "4"]}], "-", 
       RowBox[{"441", " ", 
        SuperscriptBox["#1", "5"]}], "+", 
       SuperscriptBox["#1", "6"]}], "&"}], ",", "3"}], "]"}], ",", 
   RowBox[{"Root", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"518400", "-", 
       RowBox[{"1531872", " ", "#1"}], "+", 
       RowBox[{"993560", " ", 
        SuperscriptBox["#1", "2"]}], "-", 
       RowBox[{"219492", " ", 
        SuperscriptBox["#1", "3"]}], "+", 
       RowBox[{"17836", " ", 
        SuperscriptBox["#1", "4"]}], "-", 
       RowBox[{"441", " ", 
        SuperscriptBox["#1", "5"]}], "+", 
       SuperscriptBox["#1", "6"]}], "&"}], ",", "2"}], "]"}], ",", 
   RowBox[{"Root", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"518400", "-", 
       RowBox[{"1531872", " ", "#1"}], "+", 
       RowBox[{"993560", " ", 
        SuperscriptBox["#1", "2"]}], "-", 
       RowBox[{"219492", " ", 
        SuperscriptBox["#1", "3"]}], "+", 
       RowBox[{"17836", " ", 
        SuperscriptBox["#1", "4"]}], "-", 
       RowBox[{"441", " ", 
        SuperscriptBox["#1", "5"]}], "+", 
       SuperscriptBox["#1", "6"]}], "&"}], ",", "1"}], "]"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.6586398073782635`*^9}],

Cell[BoxData[
 RowBox[{"N", "[", "%", "]"}]], "Input",
 CellChangeTimes->{{3.6586356180406466`*^9, 3.658635619907754*^9}}],

Cell[BoxData[
 StyleBox[
  RowBox[{"{", 
   RowBox[{
   "397.5032850980498`", ",", "25.926618845715986`", ",", 
    "9.857141444986159`", ",", "5.090499088899524`", ",", 
    "2.1579025994774916`", ",", "0.4645529228710743`"}], "}"}],
  FontSize->24]], "Input",
 CellChangeTimes->{3.658639822953154*^9}],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{
   RowBox[{
    RowBox[{"f", "[", 
     RowBox[{"i_", ",", "j_"}], "]"}], ":=", 
    RowBox[{"Min", "[", 
     RowBox[{"i", ",", "j"}], "]"}]}], ";", 
   RowBox[{"B", "=", 
    RowBox[{"Array", "[", 
     RowBox[{"f", ",", 
      RowBox[{"{", 
       RowBox[{"5", ",", "5"}], "}"}]}], "]"}]}]}],
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6586361242035975`*^9, 3.6586361703942394`*^9}, {
  3.6586362070423355`*^9, 3.6586362086734295`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"1", ",", "1", ",", "1", ",", "1", ",", "1"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1", ",", "2", ",", "2", ",", "2", ",", "2"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1", ",", "2", ",", "3", ",", "3", ",", "3"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1", ",", "2", ",", "3", ",", "4", ",", "4"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1", ",", "2", ",", "3", ",", "4", ",", "5"}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.658636171430299*^9, 3.658636210820552*^9, 
  3.6586399815222235`*^9}]
}, Open  ]],

Cell[BoxData[
 StyleBox[
  RowBox[{"B", " ", "//", "MatrixForm"}],
  FontSize->24]], "Input",
 CellChangeTimes->{{3.658636174632482*^9, 3.6586361836829996`*^9}}],

Cell[BoxData[
 StyleBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {"1", "1", "1", "1", "1"},
      {"1", "2", "2", "2", "2"},
      {"1", "2", "3", "3", "3"},
      {"1", "2", "3", "4", "4"},
      {"1", "2", "3", "4", "5"}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "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$, 
    MatrixForm[BoxForm`e$]]],
  FontSize->24]], "Input",
 CellChangeTimes->{3.6586400043405285`*^9}],

Cell[BoxData[
 StyleBox[
  RowBox[{"MatrixForm", "[", 
   RowBox[{"Inverse", "[", "B", "]"}], "]"}],
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6586361949296427`*^9, 3.6586362263744416`*^9}}],

Cell[BoxData[
 StyleBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {"2", 
       RowBox[{"-", "1"}], "0", "0", "0"},
      {
       RowBox[{"-", "1"}], "2", 
       RowBox[{"-", "1"}], "0", "0"},
      {"0", 
       RowBox[{"-", "1"}], "2", 
       RowBox[{"-", "1"}], "0"},
      {"0", "0", 
       RowBox[{"-", "1"}], "2", 
       RowBox[{"-", "1"}]},
      {"0", "0", "0", 
       RowBox[{"-", "1"}], "1"}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "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$, 
    MatrixForm[BoxForm`e$]]],
  FontSize->24]], "Input",
 CellChangeTimes->{3.658640028023884*^9}],

Cell[BoxData[
 StyleBox[
  RowBox[{"S", "=", 
   RowBox[{
    RowBox[{"SparseArray", "[", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"5", ",", "5"}], "}"}], "\[Rule]", 
       RowBox[{"-", "1"}]}], "}"}], "]"}], " ", "//", " ", "MatrixForm"}]}],
  FontSize->24]], "Input",
 CellChangeTimes->{{3.65863705453181*^9, 3.658637107473838*^9}}],

Cell[BoxData[
 StyleBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {"0", "0", "0", "0", "0"},
      {"0", "0", "0", "0", "0"},
      {"0", "0", "0", "0", "0"},
      {"0", "0", "0", "0", "0"},
      {"0", "0", "0", "0", 
       RowBox[{"-", "1"}]}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "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[
    SparseArray[
     Automatic, {5, 5}, 0, {1, {{0, 0, 0, 0, 0, 1}, {{5}}}, {-1}}]]]],
  FontSize->24]], "Input",
 CellChangeTimes->{3.6586403500663033`*^9}],

Cell[BoxData[
 StyleBox[
  RowBox[{"G", "=", 
   RowBox[{
    RowBox[{"SparseArray", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{
         RowBox[{"Band", "[", 
          RowBox[{"{", 
           RowBox[{"1", ",", "1"}], "}"}], "]"}], "\[Rule]", "2"}], ",", 
        RowBox[{
         RowBox[{"Band", "[", 
          RowBox[{"{", 
           RowBox[{"2", ",", "1"}], "}"}], "]"}], "\[Rule]", 
         RowBox[{"-", "1"}]}], ",", 
        RowBox[{
         RowBox[{"Band", "[", 
          RowBox[{"{", 
           RowBox[{"1", ",", "2"}], "}"}], "]"}], "\[Rule]", 
         RowBox[{"-", "1"}]}]}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"5", ",", "5"}], "}"}]}], "]"}], "//", "MatrixForm"}]}],
  FontSize->24]], "Input",
 CellChangeTimes->{{3.658636856650491*^9, 3.658636941021317*^9}}],

Cell[BoxData[
 StyleBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {"2", 
       RowBox[{"-", "1"}], "0", "0", "0"},
      {
       RowBox[{"-", "1"}], "2", 
       RowBox[{"-", "1"}], "0", "0"},
      {"0", 
       RowBox[{"-", "1"}], "2", 
       RowBox[{"-", "1"}], "0"},
      {"0", "0", 
       RowBox[{"-", "1"}], "2", 
       RowBox[{"-", "1"}]},
      {"0", "0", "0", 
       RowBox[{"-", "1"}], "2"}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "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[
    SparseArray[
     Automatic, {5, 5}, 0, {
      1, {{0, 2, 5, 8, 11, 13}, {{2}, {1}, {1}, {2}, {3}, {4}, {2}, {3}, {
        3}, {5}, {4}, {4}, {5}}}, {-1, 2, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1,
        2}}]]]],
  FontSize->24]], "Input",
 CellChangeTimes->{3.6586404095127034`*^9}],

Cell[BoxData[
 StyleBox[
  RowBox[{"MatrixForm", "[", 
   RowBox[{"IdentityMatrix", "[", "5", "]"}], "]"}],
  FontSize->24]], "Input",
 CellChangeTimes->{{3.658640417300149*^9, 3.6586404536432276`*^9}}],

Cell[BoxData[
 StyleBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {"1", "0", "0", "0", "0"},
      {"0", "1", "0", "0", "0"},
      {"0", "0", "1", "0", "0"},
      {"0", "0", "0", "1", "0"},
      {"0", "0", "0", "0", "1"}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "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$, 
    MatrixForm[BoxForm`e$]]],
  FontSize->24]], "Input",
 CellChangeTimes->{3.6586404638328104`*^9}],

Cell[BoxData[
 StyleBox[
  RowBox[{"MatrixForm", "[", 
   RowBox[{"DiagonalMatrix", "[", 
    RowBox[{"{", 
     RowBox[{"1", ",", 
      RowBox[{"1", "/", "2"}], ",", 
      RowBox[{"1", "/", "3"}], ",", 
      RowBox[{"1", "/", "4"}], ",", 
      RowBox[{"1", "/", "5"}]}], "}"}], "]"}], "]"}],
  FontSize->24]], "Input",
 CellChangeTimes->{{3.658640480872785*^9, 3.658640547201579*^9}}],

Cell[BoxData[
 StyleBox[
  TagBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
      {"1", "0", "0", "0", "0"},
      {"0", 
       FractionBox["1", "2"], "0", "0", "0"},
      {"0", "0", 
       FractionBox["1", "3"], "0", "0"},
      {"0", "0", "0", 
       FractionBox["1", "4"], "0"},
      {"0", "0", "0", "0", 
       FractionBox["1", "5"]}
     },
     GridBoxAlignment->{
      "Columns" -> {{Center}}, "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$, 
    MatrixForm[BoxForm`e$]]],
  FontSize->24]], "Input",
 CellChangeTimes->{3.658640563647519*^9}],

Cell[BoxData[
 StyleBox[
  RowBox[{"ChebyshevT", "[", 
   RowBox[{"5", ",", "x"}], "]"}],
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6586405838526754`*^9, 3.6586406019017076`*^9}}],

Cell[BoxData[
 StyleBox[
  RowBox[{
   RowBox[{"5", " ", "x"}], "-", 
   RowBox[{"20", " ", 
    SuperscriptBox["x", "3"]}], "+", 
   RowBox[{"16", " ", 
    SuperscriptBox["x", "5"]}]}],
  FontSize->24]], "Input",
 CellChangeTimes->{3.6586406319614267`*^9}],

Cell[BoxData[
 RowBox[{"Plot", "[", 
  StyleBox[
   RowBox[{
    RowBox[{
     RowBox[{"5", " ", "x"}], "-", 
     RowBox[{"20", " ", 
      SuperscriptBox["x", "3"]}], "+", 
     RowBox[{"16", " ", 
      SuperscriptBox["x", "5"]}]}], ",", 
    RowBox[{"{", 
     RowBox[{"x", ",", 
      RowBox[{"-", "1"}], ",", "1"}], "}"}]}],
   FontSize->24], 
  StyleBox["]",
   FontSize->24]}]], "Input",
 CellChangeTimes->{{3.658640640724928*^9, 3.658640667128438*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwtmnk0Ve/3xzUpjZKpUoSi0RAZSltSSaFRKCWlJEmKNJA5U4gG+ShKkTGh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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  ImageSize->{618., Automatic},
  PlotRange->{{-1, 1}, {-0.9999999973888798, 0.9999996926789017}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{3.658640670115609*^9}],

Cell[BoxData[
 StyleBox[
  RowBox[{"ChebyshevU", "[", 
   RowBox[{"5", ",", "x"}], "]"}],
  FontSize->24]], "Input",
 CellChangeTimes->{3.6586407858102264`*^9}],

Cell[BoxData[
 StyleBox[
  RowBox[{
   RowBox[{"6", " ", "x"}], "-", 
   RowBox[{"32", " ", 
    SuperscriptBox["x", "3"]}], "+", 
   RowBox[{"32", " ", 
    SuperscriptBox["x", "5"]}]}],
  FontSize->24]], "Input",
 CellChangeTimes->{3.6586407992719965`*^9}],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"LegendreP", "[", 
   RowBox[{"6", ",", "x"}], "]"}],
  FontSize->24]], "Input",
 CellChangeTimes->{{3.658641339240881*^9, 3.6586413498474874`*^9}}],

Cell[BoxData[
 RowBox[{
  FractionBox["1", "16"], " ", 
  RowBox[{"(", 
   RowBox[{
    RowBox[{"-", "5"}], "+", 
    RowBox[{"105", " ", 
     SuperscriptBox["x", "2"]}], "-", 
    RowBox[{"315", " ", 
     SuperscriptBox["x", "4"]}], "+", 
    RowBox[{"231", " ", 
     SuperscriptBox["x", "6"]}]}], ")"}]}]], "Output",
 CellChangeTimes->{3.658641360015069*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 StyleBox[
  RowBox[{"Plot", "[", 
   RowBox[{
    RowBox[{
     FractionBox["1", "16"], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "5"}], "+", 
       RowBox[{"105", " ", 
        SuperscriptBox["x", "2"]}], "-", 
       RowBox[{"315", " ", 
        SuperscriptBox["x", "4"]}], "+", 
       RowBox[{"231", " ", 
        SuperscriptBox["x", "6"]}]}], ")"}]}], ",", 
    RowBox[{"{", 
     RowBox[{"x", ",", 
      RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "]"}],
  FontSize->24]], "Input",
 CellChangeTimes->{{3.6586413652683697`*^9, 3.6586413833984065`*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJw1m3k41N/7/ymEJGmPJCFJhSSUbvWWRCQhIqRFJZGypGQJoRKSVNZISUWR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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{{-1, 1}, {-0.4147504531371, 0.9999991428573161}},
  PlotRangeClipping->True,
  PlotRangePadding->{
    Scaled[0.02], 
    Scaled[0.02]}]], "Output",
 CellChangeTimes->{3.658641396537158*^9}]
}, Open  ]],

Cell[BoxData[
 StyleBox[
  RowBox[{"Simplify", "[", 
   RowBox[{
    RowBox[{
     FractionBox["1", "16"], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "5"}], "+", 
       RowBox[{"105", " ", 
        SuperscriptBox["x", "2"]}], "-", 
       RowBox[{"315", " ", 
        SuperscriptBox["x", "4"]}], "+", 
       RowBox[{"231", " ", 
        SuperscriptBox["x", "6"]}]}], ")"}]}], 
    StyleBox[
     RowBox[{"/", "."}]], 
    RowBox[{"x", "\[Rule]", "1"}]}], "]"}],
  FontSize->24]], "Input",
 CellChangeTimes->{{3.658641429560047*^9, 3.658641446276003*^9}}],

Cell[BoxData[
 StyleBox["1",
  FontSize->24]], "Input",
 CellChangeTimes->{3.658641457658654*^9}]
},
WindowSize->{1350, 633},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
FrontEndVersion->"8.0 for Microsoft Windows (64-bit) (November 7, 2010)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[557, 20, 394, 9, 52, "Input"],
Cell[CellGroupData[{
Cell[976, 33, 209, 6, 42, "Input"],
Cell[1188, 41, 176, 4, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[1401, 50, 406, 12, 42, "Input"],
Cell[1810, 64, 258, 8, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[2105, 77, 192, 5, 42, "Input"],
Cell[2300, 84, 677, 19, 43, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[3014, 108, 204, 6, 42, "Input"],
Cell[3221, 116, 166, 4, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[3424, 125, 231, 7, 42, "Input"],
Cell[3658, 134, 121, 2, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[3816, 141, 222, 7, 42, "Input"],
Cell[4041, 150, 168, 4, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4246, 159, 199, 6, 42, "Input"],
Cell[4448, 167, 212, 7, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4697, 179, 289, 9, 42, "Input"],
Cell[4989, 190, 242, 6, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[5268, 201, 277, 9, 42, "Input"],
Cell[5548, 212, 164, 4, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[5749, 221, 244, 9, 42, "Input"],
Cell[5996, 232, 189, 5, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[6222, 242, 173, 5, 42, "Input"],
Cell[6398, 249, 287, 9, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[6722, 263, 175, 5, 42, "Input"],
Cell[6900, 270, 265, 9, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[7202, 284, 214, 6, 42, "Input"],
Cell[7419, 292, 1044, 32, 48, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[8500, 329, 183, 5, 42, "Input"],
Cell[8686, 336, 364, 12, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[9087, 353, 218, 6, 42, "Input"],
Cell[9308, 361, 366, 12, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[9711, 378, 182, 5, 42, "Input"],
Cell[9896, 385, 179, 5, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[10112, 395, 229, 6, 42, "Input"],
Cell[10344, 403, 680, 19, 43, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[11061, 427, 261, 7, 42, "Input"],
Cell[11325, 436, 838, 30, 48, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[12200, 471, 222, 6, 42, "Input"],
Cell[12425, 479, 237, 7, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[12699, 491, 243, 7, 42, "Input"],
Cell[12945, 500, 213, 7, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[13195, 512, 663, 20, 62, "Input"],
Cell[13861, 534, 518, 17, 47, "Output"],
Cell[14382, 553, 115, 2, 47, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[14534, 560, 223, 6, 42, "Input"],
Cell[14760, 568, 781, 23, 57, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[15578, 596, 559, 18, 62, "Input"],
Cell[16140, 616, 795, 26, 47, "Output"],
Cell[16938, 644, 120, 2, 47, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[17095, 651, 219, 6, 42, "Input"],
Cell[17317, 659, 941, 28, 72, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[18295, 692, 414, 12, 62, "Input"],
Cell[18712, 706, 304, 9, 30, "Output"],
Cell[19019, 717, 413, 11, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[19469, 733, 733, 22, 87, "Input"],
Cell[20205, 757, 328, 9, 30, "Output"],
Cell[20536, 768, 385, 13, 47, "Output"],
Cell[20924, 783, 1175, 42, 47, "Output"]
}, Open  ]],
Cell[22114, 828, 122, 2, 31, "Input"],
Cell[CellGroupData[{
Cell[22261, 834, 502, 15, 87, "Input"],
Cell[22766, 851, 342, 9, 30, "Output"],
Cell[23111, 862, 245, 5, 33, "Output"],
Cell[23359, 869, 575, 16, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[23971, 890, 286, 9, 42, "Input"],
Cell[24260, 901, 848, 27, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[25145, 933, 212, 6, 42, "Input"],
Cell[25360, 941, 3481, 117, 69, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[28878, 1063, 369, 12, 42, "Input"],
Cell[29250, 1077, 118, 2, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[29405, 1084, 183, 5, 42, "Input"],
Cell[29591, 1091, 118, 2, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[29746, 1098, 212, 6, 42, "Input"],
Cell[29961, 1106, 1497, 51, 33, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[31495, 1162, 177, 5, 42, "Input"],
Cell[31675, 1169, 345, 11, 33, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[32057, 1185, 260, 9, 67, "Input"],
Cell[32320, 1196, 255, 7, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[32612, 1208, 216, 6, 42, "Input"],
Cell[32831, 1216, 296, 8, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[33164, 1229, 191, 5, 42, "Input"],
Cell[33358, 1236, 300, 8, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[33695, 1249, 192, 5, 42, "Input"],
Cell[33890, 1256, 311, 8, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[34238, 1269, 184, 5, 42, "Input"],
Cell[34425, 1276, 311, 8, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[34773, 1289, 471, 14, 36, "Input"],
Cell[35247, 1305, 821, 22, 30, "Output"]
}, Open  ]],
Cell[36083, 1330, 160, 4, 36, "Input"],
Cell[36246, 1336, 893, 24, 142, "Input"],
Cell[37142, 1362, 755, 22, 98, "Input"],
Cell[37900, 1386, 196, 5, 36, "Input"],
Cell[38099, 1393, 1501, 49, 265, "Input"],
Cell[39603, 1444, 1128, 37, 146, "Input"],
Cell[CellGroupData[{
Cell[40756, 1485, 158, 4, 42, "Input"],
Cell[40917, 1491, 120, 2, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[41074, 1498, 151, 4, 42, "Input"],
Cell[41228, 1504, 99, 1, 30, "Output"]
}, Open  ]],
Cell[41342, 1508, 161, 4, 36, "Input"],
Cell[41506, 1514, 3020, 88, 77, "Input"],
Cell[44529, 1604, 3022, 88, 77, "Output"],
Cell[47554, 1694, 122, 2, 31, "Input"],
Cell[47679, 1698, 303, 8, 77, "Input"],
Cell[CellGroupData[{
Cell[48007, 1710, 481, 15, 42, "Input"],
Cell[48491, 1727, 592, 15, 30, "Output"]
}, Open  ]],
Cell[49098, 1745, 161, 4, 42, "Input"],
Cell[49262, 1751, 802, 23, 157, "Input"],
Cell[50067, 1776, 197, 5, 42, "Input"],
Cell[50267, 1783, 984, 31, 157, "Input"],
Cell[51254, 1816, 366, 11, 42, "Input"],
Cell[51623, 1829, 899, 26, 157, "Input"],
Cell[52525, 1857, 822, 25, 42, "Input"],
Cell[53350, 1884, 1189, 36, 157, "Input"],
Cell[54542, 1922, 202, 5, 42, "Input"],
Cell[54747, 1929, 802, 23, 157, "Input"],
Cell[55552, 1954, 389, 11, 42, "Input"],
Cell[55944, 1967, 904, 27, 209, "Input"],
Cell[56851, 1996, 186, 5, 42, "Input"],
Cell[57040, 2003, 258, 9, 44, "Input"],
Cell[57301, 2014, 461, 16, 48, "Input"],
Cell[57765, 2032, 14768, 248, 397, "Output"],
Cell[72536, 2282, 160, 5, 42, "Input"],
Cell[72699, 2289, 258, 9, 44, "Input"],
Cell[CellGroupData[{
Cell[72982, 2302, 183, 5, 42, "Input"],
Cell[73168, 2309, 363, 12, 47, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[73568, 2326, 589, 19, 71, "Input"],
Cell[74160, 2347, 17442, 292, 238, "Output"]
}, Open  ]],
Cell[91617, 2642, 573, 19, 71, "Input"],
Cell[92193, 2663, 97, 3, 42, "Input"]
}
]
*)

(* End of internal cache information *)