Mathematica (linear algebra) 4 tasks

profileridasak
thechallenge.nb

(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 11.3' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 58261, 1568] NotebookOptionsPosition[ 47457, 1399] NotebookOutlinePosition[ 47829, 1415] CellTagsIndexPosition[ 47786, 1412] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell["1.", "Text", CellChangeTimes->{{3.7543064517934995`*^9, 3.7543064597839565`*^9}},ExpressionUUID->"0f82b4d3-d3f5-4cc9-a373-\ 8d47a4158ede"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"A", " ", "=", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "2"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"3", ",", "4", ",", RowBox[{"-", "3"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"1", ",", "2", ",", "1"}], "}"}]}], "}"}]}]], "Input", CellChangeTimes->{{3.7543061762427387`*^9, 3.7543061811310186`*^9}, { 3.754306244549646*^9, 3.75430627819457*^9}}, CellLabel-> "In[118]:=",ExpressionUUID->"4ad0458f-cc24-4891-b649-6a2d96f73ea5"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "4", ",", RowBox[{"-", "3"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "1"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.755630635444068*^9}, CellLabel-> "Out[118]=",ExpressionUUID->"a5071cc4-e505-434b-8294-be948a750e31"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "4", ",", RowBox[{"-", "3"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "1"}], "}"}]}], "}"}], "//", "MatrixForm"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.754306282618823*^9, 3.754306306238174*^9}}, CellLabel->"In[14]:=",ExpressionUUID->"ead1c6a5-6651-4468-98dc-f6ae2b28b6fd"], Cell["\<\ a) \ \>", "Text", CellChangeTimes->{{3.7556306819347267`*^9, 3.7556306830157886`*^9}, 3.755630929069862*^9},ExpressionUUID->"214100a1-4536-4115-b83e-\ ea1110fa4245"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"B1", " ", "=", " ", RowBox[{"(", GridBox[{ {"1"}, {"1"}, {"2"} }], ")"}]}]], "Input", CellLabel-> "In[124]:=",ExpressionUUID->"2fb1c822-76f1-4c2f-b8c0-b164c5d3683e"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", "1", "}"}], ",", RowBox[{"{", "1", "}"}], ",", RowBox[{"{", "2", "}"}]}], "}"}]], "Output", CellChangeTimes->{3.7556309514871445`*^9}, CellLabel-> "Out[124]=",ExpressionUUID->"d2b26b3c-0b70-438e-8e62-687ae9b9837b"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"B2", " ", "=", " ", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1"}, {"1"}, { RowBox[{"-", "1"}]} }], "\[NoBreak]", ")"}]}]], "Input", CellLabel-> "In[123]:=",ExpressionUUID->"c681438f-5f4f-4276-b1ae-ed4ce1d738a1"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", "1", "}"}], ",", RowBox[{"{", "1", "}"}], ",", RowBox[{"{", RowBox[{"-", "1"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.7556309343151617`*^9}, CellLabel-> "Out[123]=",ExpressionUUID->"2d97afb5-fd21-469f-a36c-802840b83d2f"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"LinearSolve", "[", RowBox[{"A", ",", " ", "B1"}], "]"}]], "Input", CellChangeTimes->{{3.7556306111076756`*^9, 3.7556306215572734`*^9}, { 3.7556308557146664`*^9, 3.7556308712615557`*^9}},ExpressionUUID->"138995e0-6e43-459a-b5a7-\ aad0a914e1ca"], Cell[BoxData[ TemplateBox[{ "LinearSolve","nosol", "\"Linear equation encountered that has no solution.\"",2,120,30, 17107823090595042059,"Local"}, "MessageTemplate"]], "Message", "MSG", CellChangeTimes->{3.7556306405843616`*^9}, CellLabel-> "During evaluation of \ In[120]:=",ExpressionUUID->"a8cc029c-0c60-46c5-8467-8a9c925d8287"], Cell[BoxData[ RowBox[{"LinearSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "4", ",", RowBox[{"-", "3"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "1"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "1", "}"}], ",", RowBox[{"{", "1", "}"}], ",", RowBox[{"{", "2", "}"}]}], "}"}]}], "]"}]], "Output", CellChangeTimes->{{3.755630613293801*^9, 3.7556306405873623`*^9}}, CellLabel-> "Out[120]=",ExpressionUUID->"98ab04e7-6835-4ecd-8c56-665da4a55227"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"LinearSolve", "[", RowBox[{"A", ",", " ", "B2"}], "]"}]], "Input", CellChangeTimes->{{3.755630688339093*^9, 3.75563068932615*^9}, { 3.755630883254242*^9, 3.755630886702439*^9}}, CellLabel-> "In[122]:=",ExpressionUUID->"5400ab28-5ee3-43f4-9d91-38317eb8330e"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", "3", "}"}], ",", RowBox[{"{", RowBox[{"-", "2"}], "}"}], ",", RowBox[{"{", "0", "}"}]}], "}"}]], "Output", CellChangeTimes->{3.755630890860677*^9}, CellLabel-> "Out[122]=",ExpressionUUID->"95ebd737-e5a3-4c18-b475-9d9bd8accf97"] }, Open ]], Cell[BoxData[ RowBox[{"MatrixRank", "[", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "1", RowBox[{"-", "2"}]}, {"3", "4", RowBox[{"-", "3"}]}, {"1", "2", "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]", ")"}], "]"}]], "Text", "Input", CellChangeTimes->{{3.755630599959038*^9, 3.7556306008890915`*^9}, { 3.755630879082003*^9, 3.755630879261013*^9}, {3.7556309190302877`*^9, 3.755630920901395*^9}, {3.7556309984488306`*^9, 3.755630999398885*^9}, { 3.755631124377033*^9, 3.755631138386834*^9}}, CellLabel-> "In[125]:=",ExpressionUUID->"447c094b-2493-42bb-94e0-a01c4eede6ac"], Cell[BoxData["2"], "Output", CellChangeTimes->{3.755631178311118*^9}, CellLabel-> "Out[125]=",ExpressionUUID->"1666efba-610e-4536-a02c-5229e2b59d39"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.7543064734747396`*^9, 3.754306475242841*^9}, { 3.7543066871479607`*^9, 3.7543066873279715`*^9}, {3.7556307955962276`*^9, 3.755630846723152*^9}, 3.7556309375223455`*^9},ExpressionUUID->"2d80a300-14ab-44c2-be1a-\ 24c3c9515f39"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.755630940100493*^9, 3.7556309401104937`*^9}},ExpressionUUID->"ad214f94-4531-4380-ba5f-\ c2ae41e6f8fe"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.7543062909272985`*^9, 3.7543062909342985`*^9}, { 3.754306745017271*^9, 3.7543067455573015`*^9}, {3.754306824075793*^9, 3.7543069990127983`*^9}, 3.7556309558703947`*^9},ExpressionUUID->"51fe52ff-e512-417e-813d-\ 8762a79cf229"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.7556309573294783`*^9, 3.7556309583085346`*^9}},ExpressionUUID->"0ff394c9-e76e-483b-be35-\ 6ad51b963f8e"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.754306925343585*^9, 3.7543069253545856`*^9}, { 3.7543070109514813`*^9, 3.7543071058109074`*^9}, {3.7543071564498034`*^9, 3.754307178529066*^9}, {3.754307215680191*^9, 3.754307237957465*^9}, { 3.7543073242263994`*^9, 3.754307338377209*^9}, {3.7543076657179317`*^9, 3.7543076748394537`*^9}, 3.7556311409079785`*^9},ExpressionUUID->"d451e8dc-c133-4b59-8935-\ 8f1177c510aa"], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{ 3.7543090101318283`*^9},ExpressionUUID->"57612376-b42c-40d5-8de1-\ 9023a91f614b"], Cell[TextData[StyleBox["2.", FontWeight->"Bold"]], "Text", CellChangeTimes->{{3.7543090274288173`*^9, 3.754309041864643*^9}},ExpressionUUID->"ac73dec3-6884-4aa0-8990-\ b33854f00cb7"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.754309054331356*^9, 3.75430905596445*^9}},ExpressionUUID->"243547ad-639d-493f-9033-\ 27f62c83fcea"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"X", "=", RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "2", "2"}, {"1", "0", "4"}, {"2", "2", "4"} }], "\[NoBreak]", ")"}]}]], "Input", CellChangeTimes->{{3.754309123334303*^9, 3.7543091352829866`*^9}, { 3.754309180000544*^9, 3.7543092273512526`*^9}, {3.75430925948009*^9, 3.7543092617612205`*^9}, {3.754309515725746*^9, 3.754309520583024*^9}}, CellLabel->"In[53]:=",ExpressionUUID->"a5cd3a9b-4c6a-4a12-a6fc-db27d0b1642f"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "2", ",", "4"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.754309264814395*^9, 3.754309552128828*^9}, CellLabel->"Out[53]=",ExpressionUUID->"a8969f12-1e30-4868-8844-c678031e4322"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Y", "=", " ", RowBox[{"(", "\[NoBreak]", GridBox[{ {"3", "4", "5"}, {"2", "6", "1"}, {"3", "2", "1"} }], "\[NoBreak]", ")"}]}]], "Input", CellChangeTimes->{{3.7543092919079447`*^9, 3.754309340477723*^9}, { 3.7543095298745556`*^9, 3.7543095493636703`*^9}}, CellLabel->"In[54]:=",ExpressionUUID->"3e01a96e-99ca-4740-873a-c3954edd737e"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"3", ",", "4", ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "6", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "2", ",", "1"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.754309344005924*^9, 3.754309554321954*^9}, CellLabel->"Out[54]=",ExpressionUUID->"ceded3cc-02ce-4b1c-896f-28fc5b594962"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"X", ".", "Y"}], "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.7543093526604195`*^9, 3.75430936665722*^9}, { 3.754309613802356*^9, 3.754309614062371*^9}}, CellLabel->"In[57]:=",ExpressionUUID->"5e904637-5b7a-4a8f-b254-634c36df03a3"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"13", "20", "9"}, {"15", "12", "9"}, {"22", "28", "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$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.7543095584431896`*^9, 3.7543096163865037`*^9}, CellLabel-> "Out[57]//MatrixForm=",ExpressionUUID->"193adc2f-5c87-4491-9e62-\ 6dbbccde3da4"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"Y", ".", "X"}], "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.7543093888664904`*^9, 3.7543093914666395`*^9}, { 3.754309610862188*^9, 3.7543096110511985`*^9}}, CellLabel->"In[58]:=",ExpressionUUID->"fed3e554-b1af-4902-afe6-356f7f3f29bd"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"17", "16", "42"}, {"10", "6", "32"}, {"7", "8", "18"} }, 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$, MatrixForm[BoxForm`e$]]]], "Input", CellChangeTimes->{{3.7543097964478025`*^9, 3.754309808756507*^9}},ExpressionUUID->"70692a0a-6668-4bea-84c9-\ 6ec01064ab16"], Cell[TextData[StyleBox["3.", FontWeight->"Bold"]], "Text", CellChangeTimes->{{3.7543098217372494`*^9, 3.754309822856313*^9}},ExpressionUUID->"7eb3a044-02f9-4ae1-9b9c-\ 115b3e265e45"], Cell[BoxData[ RowBox[{ RowBox[{"ri", ":=", RowBox[{"RandomInteger", "[", RowBox[{"{", RowBox[{"0", ",", " ", "9"}], "}"}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.754309830878772*^9, 3.754309832467863*^9}, { 3.75430986405567*^9, 3.75430989693655*^9}}, CellLabel->"In[59]:=",ExpressionUUID->"16729cba-3ae2-4b0e-b9aa-71f725a2495f"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"A", "=", " ", RowBox[{ RowBox[{"Table", "[", RowBox[{"ri", ",", RowBox[{"{", RowBox[{"j", ",", " ", "1", ",", " ", "3"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"k", ",", " ", "1", ",", " ", "5"}], "}"}]}], "]"}], "//", "MatrixForm"}]}]], "Input", CellChangeTimes->{{3.754309965365464*^9, 3.7543100197615757`*^9}}, CellLabel->"In[61]:=",ExpressionUUID->"e0ee5f99-2352-466f-b5bc-ae808dc8a7d9"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"5", "2", "3", "6", "4"}, {"0", "4", "5", "4", "7"}, {"9", "3", "9", "1", "3"} }, 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->{{3.7543100130661926`*^9, 3.7543100200275908`*^9}}, CellLabel-> "Out[61]//MatrixForm=",ExpressionUUID->"05482d83-4fae-4512-8aa2-\ 2d92abc551a5"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"B", " ", "=", " ", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"5", "2", "3", "6", "4"}, {"0", "4", "5", "4", "7"}, {"9", "3", "9", "1", "3"} }, 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$, MatrixForm[BoxForm`e$]]]}]], "Input", CellChangeTimes->{{3.754310093481792*^9, 3.7543100946608596`*^9}}, CellLabel->"In[62]:=",ExpressionUUID->"4ffc188b-efa7-4770-842a-e7c45e63e73e"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"5", ",", "2", ",", "3", ",", "6", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "4", ",", "5", ",", "4", ",", "7"}], "}"}], ",", RowBox[{"{", RowBox[{"9", ",", "3", ",", "9", ",", "1", ",", "3"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.7543100967839813`*^9}, CellLabel->"Out[62]=",ExpressionUUID->"6a4ac5ed-2eea-42a0-bf78-89197f1b89ea"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"RowReduce", "[", "B", "]"}], "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.7543101369502783`*^9, 3.7543101555573425`*^9}}, CellLabel->"In[64]:=",ExpressionUUID->"8c23beee-6d62-4a10-9cec-d06d8d2b2dca"], Cell[BoxData[ RowBox[{ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "0", "0", FractionBox["88", "87"], FractionBox["5", "29"]}, {"0", "1", "0", FractionBox["317", "87"], FractionBox["77", "29"]}, {"0", "0", "1", RowBox[{"-", FractionBox["184", "87"]}], RowBox[{"-", FractionBox["21", "29"]}]} }, 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$, MatrixForm[BoxForm`e$]]], "\[IndentingNewLine]"}]], "Text", "Input", CellChangeTimes->{{3.755535876319024*^9, 3.755535897489235*^9}, { 3.755535992736683*^9, 3.755536017597105*^9}},ExpressionUUID->"4bc2063b-627b-4b61-a044-\ 18e30178905f"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"r", "=", " ", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "0", "0", FractionBox["88", "87"], FractionBox["5", "29"]}, {"0", "1", "0", FractionBox["317", "87"], FractionBox["77", "29"]}, {"0", "0", "1", RowBox[{"-", FractionBox["184", "87"]}], RowBox[{"-", FractionBox["21", "29"]}]} }, 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$, MatrixForm[BoxForm`e$]]]}]], "Input", CellChangeTimes->{{3.7574192173220954`*^9, 3.757419235957161*^9}}, CellLabel->"In[2]:=",ExpressionUUID->"5d020818-6975-4e9d-a8ac-af8ffc73c6d7"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0", ",", "0", ",", FractionBox["88", "87"], ",", FractionBox["5", "29"]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0", ",", FractionBox["317", "87"], ",", FractionBox["77", "29"]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1", ",", RowBox[{"-", FractionBox["184", "87"]}], ",", RowBox[{"-", FractionBox["21", "29"]}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{{3.7574192211193123`*^9, 3.7574192380062785`*^9}}, CellLabel->"Out[2]=",ExpressionUUID->"44426ac1-d6ea-4478-bece-c1419d6cc83c"] }, Open ]], Cell[BoxData[""], "Input", CellChangeTimes->{{3.7574192668909307`*^9, 3.7574192715661983`*^9}, { 3.7574197053820105`*^9, 3.7574197753190107`*^9}, {3.757419832425277*^9, 3.757419843401905*^9}, {3.757419943086607*^9, 3.7574200667996826`*^9}, 3.757436544551156*^9},ExpressionUUID->"953d706d-4d5c-45f0-90b8-\ 14f393c92a0f"], Cell["4.", "Text", CellChangeTimes->{{3.755536032345948*^9, 3.7555360433655787`*^9}}, FontWeight->"Bold",ExpressionUUID->"e7a4ab07-7faf-4da6-af05-56593ea1f819"], Cell["\<\ a)\ \>", "Text", CellChangeTimes->{{3.757423068519371*^9, 3.757423079543002*^9}},ExpressionUUID->"5f219e44-489e-4b34-980a-\ c6db65a16cb3"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"ri", ":=", " ", RowBox[{"RandomInteger", " ", "[", RowBox[{"{", RowBox[{"0", ",", " ", "6"}], "}"}], "]"}]}], ";"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.755536113055565*^9, 3.755536169632801*^9}}, CellLabel->"In[1]:=",ExpressionUUID->"8bd178d6-fa9b-432b-aab7-743b9a47a7f6"], Cell[BoxData[ RowBox[{"V", " ", "=", " ", RowBox[{"Table", "[", RowBox[{"ri", ",", " ", RowBox[{"{", RowBox[{"j", ",", " ", "1", ",", " ", "2"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"k", ",", " ", "1", ",", " ", "2"}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.755536183015566*^9, 3.755536215553427*^9}}, CellLabel->"In[2]:=",ExpressionUUID->"cd4cc325-2c1a-4592-8800-6c1bf822e7ea"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "0"}], "}"}]}], "}"}]], "Input", CellChangeTimes->{{3.75553650670508*^9, 3.755536517684708*^9}, { 3.7555365833064613`*^9, 3.7555365992333727`*^9}},ExpressionUUID->"77956d4b-70b7-4ea7-a626-\ bf0f0e4f0ecb"], Cell["(2,2), (2,0) \[CapitalADoubleDot]r f\[ODoubleDot]rsta bas, V", "Text", CellChangeTimes->{{3.7555365840535045`*^9, 3.7555365850335608`*^9}, { 3.757422828838662*^9, 3.7574228602964616`*^9}, {3.7574229087992363`*^9, 3.7574229306454854`*^9}},ExpressionUUID->"eb9aa09c-9cde-440b-aa39-\ 6a6eacdcf2af"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"W", " ", "=", " ", RowBox[{"Table", "[", RowBox[{"ri", ",", " ", RowBox[{"{", RowBox[{"j", ",", " ", "1", ",", " ", "2"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"k", ",", " ", "1", ",", " ", "2"}], "}"}]}], "]"}]}]], "Input", CellLabel->"In[7]:=",ExpressionUUID->"7b2b2f0d-545a-413e-bd5c-71e90fc8e05b"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"3", ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "5"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.7555365915359325`*^9}, CellLabel->"Out[7]=",ExpressionUUID->"140d6718-7c30-4129-9ab4-58818c1dbf74"] }, Open ]], Cell["(3, 5), (4, 5) \[CapitalADoubleDot]r andra bas, W", "Text", CellChangeTimes->{{3.7555365707827454`*^9, 3.7555365716467943`*^9}, { 3.757422873137196*^9, 3.7574228878970404`*^9}, {3.7574229279073286`*^9, 3.7574229282873507`*^9}},ExpressionUUID->"c24646a9-fc7d-4625-8cd4-\ 37b09c27ae4f"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"x", "=", RowBox[{"{", RowBox[{"ri", ",", " ", "ri"}], "}"}]}]], "Input", CellChangeTimes->{{3.7555366179934454`*^9, 3.7555366224437*^9}, { 3.7555366591618004`*^9, 3.7555366605818815`*^9}}, CellLabel->"In[8]:=",ExpressionUUID->"ac8388e6-611c-415d-9da8-c51a7c9ba22a"], Cell[BoxData[ RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}]], "Output", CellChangeTimes->{3.7555366628740125`*^9}, CellLabel->"Out[8]=",ExpressionUUID->"ba0ff84f-5ff7-4a1d-8bb6-e86e62ce5e25"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"V", " ", "=", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "0"}], "}"}]}], "}"}]}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.755536559204083*^9, 3.755536559217084*^9}, { 3.7555367771985517`*^9, 3.7555367953495893`*^9}}, CellLabel->"In[17]:=",ExpressionUUID->"227ae1e2-b199-4abb-a169-0f442d759d22"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "0"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.755536799044801*^9, 3.7574260787575474`*^9}, CellLabel->"Out[17]=",ExpressionUUID->"f6f8b34d-fcc0-4012-aa25-a0b6d487dc38"] }, Open ]], Cell[BoxData[""], "Input", CellChangeTimes->{{3.755536557314975*^9, 3.7555365573259754`*^9}},ExpressionUUID->"1b67ae46-7155-4f7d-8f8d-\ 385480723f5f"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"W", " ", "=", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"3", ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "5"}], "}"}]}], "}"}]}]], "Input", CellChangeTimes->{{3.755536810158437*^9, 3.755536812219555*^9}}, CellLabel->"In[18]:=",ExpressionUUID->"da1e2687-ff22-46d0-86f7-1158aa74b497"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"3", ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "5"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.755536813069603*^9, 3.7574260820727367`*^9}, CellLabel->"Out[18]=",ExpressionUUID->"e840fdb5-bcc7-4ecb-ad2d-dcf81b252ee2"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"x", " ", "=", " ", RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}]}]], "Input", CellChangeTimes->{{3.7555368276584377`*^9, 3.755536829494543*^9}}, CellLabel->"In[19]:=",ExpressionUUID->"c1e8b51b-a419-487f-a44c-42eea33617fa"], Cell[BoxData[ RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}]], "Output", CellChangeTimes->{3.755536830568604*^9, 3.7574260846958866`*^9}, CellLabel->"Out[19]=",ExpressionUUID->"cb0b7fa7-28e2-4f06-9566-c9a08c16abf6"] }, Open ]], Cell[BoxData[""], "Input", CellChangeTimes->{{3.7555369046148396`*^9, 3.7555369308953424`*^9}},ExpressionUUID->"d3b4949f-9414-491f-8890-\ 7d7420c034ea"], Cell["b)", "Text", CellChangeTimes->{ 3.7555370698912926`*^9, {3.7574231312229576`*^9, 3.757423134531147*^9}},ExpressionUUID->"fec6b82a-950c-43ae-85c7-\ 11baec217615"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Graphics", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"Blue", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"V", "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "Blue", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"V", "[", RowBox[{"[", "2", "]"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "Red", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0"}], "}"}], ",", " ", "x"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", " ", "\[Rule]", " ", "True"}], ",", " ", RowBox[{"AxesLabel", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{"X", ",", "Y"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.7555371458016343`*^9, 3.7555373299871693`*^9}, { 3.7555374945255804`*^9, 3.755537550191764*^9}, {3.755537985753677*^9, 3.755537995050209*^9}, 3.755538064679191*^9, {3.75553814385772*^9, 3.755538152847234*^9}, {3.7555383233189845`*^9, 3.755538360442108*^9}, { 3.7555384626919565`*^9, 3.755538488179414*^9}, {3.7555385213573112`*^9, 3.7555385371682158`*^9}, {3.755538581208735*^9, 3.7555385813597436`*^9}, { 3.7555386200979595`*^9, 3.7555387714226146`*^9}, {3.755538809301781*^9, 3.755538816962219*^9}, {3.7555389673488207`*^9, 3.7555391099969797`*^9}, { 3.7555393025029907`*^9, 3.755539304251091*^9}}, CellLabel->"In[20]:=",ExpressionUUID->"d7d2a6b4-ac56-4d38-8cb5-81b1361d209a"], Cell[BoxData[ GraphicsBox[{ {RGBColor[0, 0, 1], ArrowBox[{{0, 0}, {2, 2}}]}, {RGBColor[0, 0, 1], ArrowBox[{{0, 0}, {2, 0}}]}, {RGBColor[1, 0, 0], ArrowBox[{{0, 0}, {1, 3}}]}}, Axes->True, AxesLabel->{ FormBox["X", TraditionalForm], FormBox["Y", TraditionalForm]}]], "Output", CellChangeTimes->{{3.7555392827678623`*^9, 3.7555393051721435`*^9}, 3.757426092023306*^9}, CellLabel->"Out[20]=",ExpressionUUID->"8511e14d-99ae-4439-88c6-56b4dbdfe087"] }, Open ]], Cell["c)", "Text", CellChangeTimes->{{3.7574244230618467`*^9, 3.757424423890894*^9}},ExpressionUUID->"866937b1-f16b-4554-b708-\ 1b29c24eb42d"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Graphics", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"Blue", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"W", "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "Blue", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"W", "[", RowBox[{"[", "2", "]"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "Red", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0"}], "}"}], ",", " ", "x"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", " ", "\[Rule]", " ", "True"}], ",", " ", RowBox[{"AxesLabel", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{"X", ",", "Y"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.755539385808756*^9, 3.7555393872698393`*^9}}, CellLabel->"In[21]:=",ExpressionUUID->"daf3b5bd-9f55-4b69-9010-4bf264c1bfd6"], Cell[BoxData[ GraphicsBox[{ {RGBColor[0, 0, 1], ArrowBox[{{0, 0}, {3, 5}}]}, {RGBColor[0, 0, 1], ArrowBox[{{0, 0}, {4, 5}}]}, {RGBColor[1, 0, 0], ArrowBox[{{0, 0}, {1, 3}}]}}, Axes->True, AxesLabel->{ FormBox["X", TraditionalForm], FormBox["Y", TraditionalForm]}]], "Output", CellChangeTimes->{3.7555394084010477`*^9, 3.7574260983486676`*^9}, CellLabel->"Out[21]=",ExpressionUUID->"312a533e-3a4f-4473-b928-d5c2e23a78e0"] }, Open ]], Cell["d)", "Text", CellChangeTimes->{{3.757424501638341*^9, 3.7574245018703547`*^9}},ExpressionUUID->"c7fb965f-9299-4363-8e55-\ ed77d0a5b56d"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"LinearSolve", "[", RowBox[{"V", ",", "x"}], " ", "]"}]], "Input", CellChangeTimes->{{3.7555396619625506`*^9, 3.755539696620533*^9}, { 3.7555397944551287`*^9, 3.7555398505383368`*^9}, 3.7555404233601*^9, { 3.755540496878305*^9, 3.755540525331932*^9}}, CellLabel->"In[22]:=",ExpressionUUID->"de5b972d-df5b-4698-857b-d0b569b5fe98"], Cell[BoxData[ RowBox[{"{", RowBox[{ FractionBox["3", "2"], ",", RowBox[{"-", "1"}]}], "}"}]], "Output", CellChangeTimes->{ 3.7555398545505657`*^9, {3.7555405003655043`*^9, 3.755540528527115*^9}, 3.757426102897928*^9}, CellLabel->"Out[22]=",ExpressionUUID->"3024182b-c2a4-4156-b5a3-dc9b2778c49c"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"LinearSolve", "[", RowBox[{"W", ",", "x"}], " ", "]"}]], "Input", CellChangeTimes->{{3.755540519551602*^9, 3.7555405265510025`*^9}}, CellLabel->"In[23]:=",ExpressionUUID->"43d87f25-60bb-4470-87b5-3272e8ae478d"], Cell[BoxData[ RowBox[{"{", RowBox[{"2", ",", RowBox[{"-", "1"}]}], "}"}]], "Output", CellChangeTimes->{3.755540531104263*^9, 3.7574261051840587`*^9}, CellLabel->"Out[23]=",ExpressionUUID->"9483113f-ba8b-4ec7-b38a-927961c5d026"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"k", "=", " ", RowBox[{"{", RowBox[{ FractionBox["3", "2"], ",", RowBox[{"-", "1"}]}], "}"}]}]], "Input", CellChangeTimes->{{3.7555413650409613`*^9, 3.755541379828807*^9}, { 3.755541783822914*^9, 3.755541785831029*^9}, 3.755542167359851*^9, 3.7555423243518305`*^9, 3.7574218256642838`*^9}, CellLabel->"In[24]:=",ExpressionUUID->"688da978-cdf4-46bb-9718-36f5bd70d6d3"], Cell[BoxData[ RowBox[{"{", RowBox[{ FractionBox["3", "2"], ",", RowBox[{"-", "1"}]}], "}"}]], "Output", CellChangeTimes->{3.7555413815669065`*^9, 3.7555418073622603`*^9, 3.7555421683819094`*^9, 3.75554232644495*^9, 3.757421830121539*^9, 3.757426107501191*^9}, CellLabel->"Out[24]=",ExpressionUUID->"e5bdb38e-d5f8-49e2-8dad-2dd096b26e4f"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"o", "=", RowBox[{"{", RowBox[{"2", ",", RowBox[{"-", "1"}]}], "}"}]}]], "Input", CellChangeTimes->{{3.7555413942206297`*^9, 3.755541429432644*^9}, { 3.755541796011611*^9, 3.7555418013719177`*^9}, 3.7555421805386047`*^9, 3.755542322960751*^9, 3.7555435418114653`*^9}, CellLabel->"In[25]:=",ExpressionUUID->"295d4aae-19ef-4389-a690-8a468a81d14e"], Cell[BoxData[ RowBox[{"{", RowBox[{"2", ",", RowBox[{"-", "1"}]}], "}"}]], "Output", CellChangeTimes->{{3.7555414105195627`*^9, 3.755541425356411*^9}, 3.7555418021409616`*^9, 3.755542181688671*^9, 3.7555423285350695`*^9, 3.75554354346356*^9, 3.7574261098853273`*^9}, CellLabel->"Out[25]=",ExpressionUUID->"3f726b04-a055-4e37-b668-3dc50ff9bf3a"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Graphics", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"Blue", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"W", "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "Blue", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"W", "[", RowBox[{"[", "2", "]"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "Red", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0"}], "}"}], ",", " ", "x"}], "}"}], "]"}], ",", "\[IndentingNewLine]", "Gray", ",", "Dashed", ",", " ", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"3", "/", "2"}], ",", RowBox[{"-", "1"}]}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "Gray", ",", "Dashed", ",", " ", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0"}], "}"}], ",", " ", "o"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", " ", "\[Rule]", " ", "True"}], ",", " ", RowBox[{"AxesLabel", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{"X", ",", "Y"}], "}"}]}]}], "]"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.755540617794221*^9, 3.755540648309966*^9}, { 3.755540781477583*^9, 3.7555408712927203`*^9}, {3.7555409081838303`*^9, 3.7555410072904987`*^9}, {3.7555410819507694`*^9, 3.7555410887651587`*^9}, {3.7555411838165956`*^9, 3.755541248494295*^9}, { 3.7555414451215415`*^9, 3.7555415519276505`*^9}, {3.755541582747413*^9, 3.7555416961048965`*^9}, 3.755541735865171*^9, {3.7555422058440523`*^9, 3.7555422648924294`*^9}, {3.755542843288512*^9, 3.755542846186678*^9}, { 3.755542877537471*^9, 3.7555428794675817`*^9}, {3.7555429208869505`*^9, 3.7555429696857414`*^9}, {3.7555430596858892`*^9, 3.755543117962222*^9}, { 3.755543181860877*^9, 3.755543187209183*^9}, {3.7555432688288517`*^9, 3.755543285638813*^9}, {3.7555433836784205`*^9, 3.7555434036045604`*^9}, { 3.7555437775469484`*^9, 3.7555438141050396`*^9}, {3.757425726566403*^9, 3.7574257788913956`*^9}, {3.7574258203407664`*^9, 3.7574258469572887`*^9}}, CellLabel->"In[26]:=",ExpressionUUID->"8218796c-f306-4dad-a44b-f1918a3224f0"], Cell[BoxData[ GraphicsBox[{ {RGBColor[0, 0, 1], ArrowBox[{{0, 0}, {3, 5}}]}, {RGBColor[0, 0, 1], ArrowBox[{{0, 0}, {4, 5}}]}, {RGBColor[1, 0, 0], ArrowBox[{{0, 0}, {1, 3}}]}, {GrayLevel[0.5], Dashing[{Small, Small}], LineBox[NCache[{{0, 0}, {Rational[3, 2], -1}}, {{0, 0}, {1.5, -1}}]]}, {GrayLevel[0.5], Dashing[{Small, Small}], LineBox[{{0, 0}, {2, -1}}]}}, Axes->True, AxesLabel->{ FormBox["X", TraditionalForm], FormBox["Y", TraditionalForm]}]], "Output", CellChangeTimes->{3.7574258549747477`*^9, 3.7574261193608694`*^9}, CellLabel->"Out[26]=",ExpressionUUID->"5b6e0904-cbee-4c0a-b259-7d315f87bd30"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Graphics", "[", "\n", RowBox[{ RowBox[{"{", RowBox[{"Blue", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"V", "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}], "]"}], ",", "\n", "Blue", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"V", "[", RowBox[{"[", "2", "]"}], "]"}]}], "}"}], "]"}], ",", "\n", "Red", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0"}], "}"}], ",", " ", "x"}], "}"}], "]"}], ",", "\n", "Gray", ",", "Dashed", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"3", "/", "2"}], ",", RowBox[{"-", "1"}]}], "}"}]}], "}"}], "]"}], ",", "\n", "Gray", ",", "Dashed", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0"}], "}"}], ",", " ", "o"}], "}"}], "]"}]}], "}"}], ",", "\n", RowBox[{"Axes", " ", "\[Rule]", " ", "True"}], ",", " ", RowBox[{"AxesLabel", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{"X", ",", "Y"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.7574262276660643`*^9, 3.757426244213011*^9}, { 3.7574263821689014`*^9, 3.757426387625213*^9}, {3.757426442011324*^9, 3.7574264434064035`*^9}, {3.7574264743301725`*^9, 3.7574264898750615`*^9}}, CellLabel->"In[32]:=",ExpressionUUID->"78129844-f92e-495e-8bb1-a2ee0a0134f5"], Cell[BoxData[ GraphicsBox[{ {RGBColor[0, 0, 1], ArrowBox[{{0, 0}, {2, 2}}]}, {RGBColor[0, 0, 1], ArrowBox[{{0, 0}, {2, 0}}]}, {RGBColor[1, 0, 0], ArrowBox[{{0, 0}, {1, 3}}]}, {GrayLevel[0.5], Dashing[{Small, Small}], ArrowBox[NCache[{{0, 0}, {Rational[3, 2], -1}}, {{0, 0}, {1.5, -1}}]]}, {GrayLevel[0.5], Dashing[{Small, Small}], ArrowBox[{{0, 0}, {2, -1}}]}}, Axes->True, AxesLabel->{ FormBox["X", TraditionalForm], FormBox["Y", TraditionalForm]}]], "Output", CellChangeTimes->{{3.7574262381816654`*^9, 3.7574262537525563`*^9}, 3.7574263941645875`*^9, 3.7574264449324913`*^9, {3.7574264751642203`*^9, 3.7574264921451917`*^9}}, CellLabel->"Out[32]=",ExpressionUUID->"e25ce515-9194-4b4c-b196-44405dc2b7cc"] }, Open ]], Cell["\<\ e) \ \>", "Text", CellChangeTimes->{{3.7556260861718645`*^9, 3.7556260886450057`*^9}, { 3.757426205929821*^9, 3.7574262242988715`*^9}},ExpressionUUID->"f6d00a4c-7269-4512-aeee-\ 10a02becf627"], Cell[BoxData[ RowBox[{"p", " ", "=", " ", RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"-", "1"}], "2"}, { RowBox[{"-", "3"}], "4"} }], "\[NoBreak]", ")"}]}]], "Input", CellChangeTimes->{{3.7556261013187304`*^9, 3.755626146700326*^9}}, CellLabel->"In[88]:=",ExpressionUUID->"a350d63c-6c1a-4e5f-8e4b-7ea8c124efd3"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "3"}], ",", "4"}], "}"}]}], "}"}]], "Input", CellChangeTimes->{{3.7556262150892377`*^9, 3.755626232818252*^9}},ExpressionUUID->"074bae88-8745-4d25-bc13-\ 38a850139cc6"], Cell[BoxData[ RowBox[{"RowReduce", "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.755626237960546*^9, 3.7556262422977943`*^9}, 3.7556269031815944`*^9},ExpressionUUID->"553e771c-08b1-4886-bc33-\ 67a0dae4d564"], Cell["5.", "Text", CellChangeTimes->{{3.7556269126231346`*^9, 3.755626922071675*^9}},ExpressionUUID->"f7aae6bd-ed36-4577-afd6-\ 9eb57127ffd0"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Graphics3D", "[", RowBox[{ RowBox[{"{", RowBox[{"Thick", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"1", ",", " ", RowBox[{"-", "1"}], ",", " ", "2"}], "}"}]}], "}"}], "]"}], ",", " ", RowBox[{"InfinitePlane", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", " ", "0", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"1", ",", " ", "1", ",", " ", "1"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", " ", "0", ",", " ", "1"}], "}"}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", " ", "\[Rule]", " ", "True"}], ",", " ", RowBox[{"AxesLabel", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{"X", ",", " ", "Y", ",", " ", "Z"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.7556269372025404`*^9, 3.7556270963296423`*^9}}, CellLabel->"In[89]:=",ExpressionUUID->"0f97f007-1aac-4dec-81e2-f41ba5d02954"], Cell[BoxData[ Graphics3DBox[ {Thickness[Large], Arrow3DBox[{{0, 0, 0}, {1, -1, 2}}], TagBox[ConicHullRegion3DBox[{{1, 0, 0}, {1, 1, 1}, {0, 0, 1}}], "InfinitePlane"]}, Axes->True, AxesLabel->{ FormBox["X", TraditionalForm], FormBox["Y", TraditionalForm], FormBox["Z", TraditionalForm]}, ImageSize->{336.89090767104284`, 450.16001249544877`}, ImageSizeRaw->Automatic, ViewPoint->{-2.5418146916615156`, 1.969876328239276, 1.0529792612849604`}, ViewVertical->{-0.2934899559178727, 0.653789013160883, 0.93359835743823}]], "Output", CellChangeTimes->{3.755627100722893*^9}, CellLabel->"Out[89]=",ExpressionUUID->"2b64d38a-717d-45f0-8ec2-112e3fc064e1"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Graphics3D", "[", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Thick", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"1", ",", " ", RowBox[{"-", "1"}], ",", " ", "2"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "Thick", ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ FractionBox["1", SqrtBox["6"]], ",", RowBox[{"-", FractionBox["1", SqrtBox["6"]]}], ",", SqrtBox[ FractionBox["2", "3"]]}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", " ", RowBox[{"InfinitePlane", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", " ", "0", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"1", ",", " ", "1", ",", " ", "1"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", " ", "0", ",", " ", "1"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", " ", "\[Rule]", " ", "True"}], ",", " ", RowBox[{"AxesLabel", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{"X", ",", " ", "Y", ",", " ", "Z"}], "}"}]}]}], "\[IndentingNewLine]", "}"}], "]"}]], "Input", CellChangeTimes->{{3.7556277409935145`*^9, 3.7556277422035837`*^9}, { 3.7556294941227875`*^9, 3.755629510674734*^9}, {3.755629606069191*^9, 3.755629727950162*^9}, {3.755629781118203*^9, 3.755629783928364*^9}, { 3.7556298290809464`*^9, 3.7556298323871355`*^9}, {3.755629869269245*^9, 3.755629899535976*^9}, {3.7556299400542936`*^9, 3.7556299555251784`*^9}, { 3.7556299909432044`*^9, 3.755630054262826*^9}}, CellLabel-> "In[114]:=",ExpressionUUID->"9b579feb-2366-4204-9af6-081a1487490c"], Cell[BoxData[ Graphics3DBox[{ {Thickness[Large], Arrow3DBox[{{0, 0, 0}, {1, -1, 2}}]}, {Thickness[Large], Arrow3DBox[ NCache[{{0, 0, 0}, { 6^Rational[-1, 2], -6^Rational[-1, 2], Rational[2, 3]^ Rational[1, 2]}}, {{0, 0, 0}, { 0.4082482904638631, -0.4082482904638631, 0.816496580927726}}]], TagBox[ConicHullRegion3DBox[{{1, 0, 0}, {1, 1, 1}, {0, 0, 1}}], "InfinitePlane"], StyleBox[{}, Axes -> True, AxesLabel -> {$CellContext`X, $CellContext`Y, $CellContext`Z}]}}, ImageSize->{427.3659759939163, 428.16751629054863`}, ImageSizeRaw->Automatic, ViewPoint->{1.386425093799253, -1.3762509046083744`, 2.762925787430483}, ViewVertical->{1.9558179556255832`, -0.20711401776461572`, 0.18157636692171764`}]], "Output", CellChangeTimes->{3.7556300559469223`*^9}, CellLabel-> "Out[114]=",ExpressionUUID->"77ced785-f44e-48d2-8a99-1056f5c7ea72"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Orthogonalize", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", " ", "0", ",", " ", "0"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"1", ",", " ", RowBox[{"-", "1"}], ",", " ", "2"}], "}"}]}], "}"}], "]"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.75562848116785*^9, 3.755628496076703*^9}, 3.7556286246330557`*^9, {3.7556293386868973`*^9, 3.755629361067178*^9}, { 3.755629404858682*^9, 3.7556294499162593`*^9}, 3.7556295776045628`*^9}, CellLabel-> "In[113]:=",ExpressionUUID->"66eaecf9-b4c5-46bc-966d-d59bacf5f2e6"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ FractionBox["1", SqrtBox["6"]], ",", RowBox[{"-", FractionBox["1", SqrtBox["6"]]}], ",", SqrtBox[ FractionBox["2", "3"]]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.7556293623652515`*^9, {3.755629407026806*^9, 3.7556294515083504`*^9}, 3.75562957983169*^9}, CellLabel-> "Out[113]=",ExpressionUUID->"4a48b9df-7931-43ce-9692-12a6254e1f4c"] }, Open ]], Cell[BoxData[""], "Input", CellChangeTimes->{{3.755629334666668*^9, 3.7556293346746683`*^9}},ExpressionUUID->"6c460b9b-1851-4647-b941-\ 883b4d4348aa"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.7556285054062366`*^9, 3.7556285076953673`*^9}, { 3.755629319656809*^9, 3.755629320827876*^9}},ExpressionUUID->"f2bd41d3-9408-42a9-b573-\ 51c287004e3f"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.755627763586807*^9, 3.75562776714301*^9}, { 3.7556278380810676`*^9, 3.755627867861771*^9}, {3.7556279664114075`*^9, 3.755628001367407*^9}, {3.7556280628079214`*^9, 3.755628095676801*^9}, { 3.7556282050360565`*^9, 3.755628225835246*^9}, {3.7556282589151382`*^9, 3.7556282759531126`*^9}, {3.7556286054649596`*^9, 3.7556286160825667`*^9}, {3.7556287454219646`*^9, 3.7556287919586267`*^9}, {3.755628906350169*^9, 3.75562892017696*^9}, 3.7556293187277555`*^9},ExpressionUUID->"102e868e-b613-46ba-93bc-\ 18db2f531e0f"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.755629317097663*^9, 3.7556293171036625`*^9}},ExpressionUUID->"a3fdd870-bea4-4d49-b2e3-\ 890f16458172"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.755627751195098*^9, 3.755627753733243*^9}},ExpressionUUID->"ae34e05a-ff1f-458b-9beb-\ 79fbb58a7a49"], Cell[BoxData[""], "Input", CellChangeTimes->{3.755628937056926*^9, 3.755629316428624*^9},ExpressionUUID->"df7deb60-dc2a-4e85-b7ae-\ 3b97c62cecdc"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.7556293156975822`*^9, 3.7556293157075834`*^9}},ExpressionUUID->"c0941a7b-aef1-44d7-9664-\ 5ccd1e465225"], Cell[BoxData[""], "Input", CellChangeTimes->{3.7556289562680244`*^9, 3.755629315017544*^9},ExpressionUUID->"234e8fcd-ca17-4f42-9f03-\ b6cd3c849229"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.755629314147494*^9, 3.7556293141544943`*^9}},ExpressionUUID->"7de34c32-b1b9-4d80-953e-\ 7fe2bd512b87"], Cell[BoxData[""], "Input", CellChangeTimes->{ 3.755629313087433*^9},ExpressionUUID->"247e5129-76b1-4bdc-b2ca-\ b87710d07a8c"] }, WindowSize->{944, 979}, WindowMargins->{{Automatic, 377}, {Automatic, 0}}, Magnification:>1.6 Inherited, FrontEndVersion->"11.3 for Microsoft Windows (64-bit) (March 6, 2018)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[558, 20, 148, 3, 55, "Text",ExpressionUUID->"0f82b4d3-d3f5-4cc9-a373-8d47a4158ede"], Cell[CellGroupData[{ Cell[731, 27, 554, 15, 45, "Input",ExpressionUUID->"4ad0458f-cc24-4891-b649-6a2d96f73ea5"], Cell[1288, 44, 427, 13, 51, "Output",ExpressionUUID->"a5071cc4-e505-434b-8294-be948a750e31"] }, Open ]], Cell[1730, 60, 537, 15, 76, "Input",ExpressionUUID->"ead1c6a5-6651-4468-98dc-f6ae2b28b6fd"], Cell[2270, 77, 180, 6, 91, "Text",ExpressionUUID->"214100a1-4536-4115-b83e-ea1110fa4245"], Cell[CellGroupData[{ Cell[2475, 87, 214, 8, 93, "Input",ExpressionUUID->"2fb1c822-76f1-4c2f-b8c0-b164c5d3683e"], Cell[2692, 97, 282, 8, 51, "Output",ExpressionUUID->"d2b26b3c-0b70-438e-8e62-687ae9b9837b"] }, Open ]], Cell[CellGroupData[{ Cell[3011, 110, 264, 9, 93, "Input",ExpressionUUID->"c681438f-5f4f-4276-b1ae-ed4ce1d738a1"], Cell[3278, 121, 302, 9, 51, "Output",ExpressionUUID->"2d97afb5-fd21-469f-a36c-802840b83d2f"] }, Open ]], Cell[CellGroupData[{ Cell[3617, 135, 276, 6, 45, "Input",ExpressionUUID->"138995e0-6e43-459a-b5a7-aad0a914e1ca"], Cell[3896, 143, 347, 9, 37, "Message",ExpressionUUID->"a8cc029c-0c60-46c5-8467-8a9c925d8287"], Cell[4246, 154, 670, 20, 51, "Output",ExpressionUUID->"98ab04e7-6835-4ecd-8c56-665da4a55227"] }, Open ]], Cell[CellGroupData[{ Cell[4953, 179, 290, 6, 45, "Input",ExpressionUUID->"5400ab28-5ee3-43f4-9d91-38317eb8330e"], Cell[5246, 187, 300, 9, 51, "Output",ExpressionUUID->"95ebd737-e5a3-4c18-b475-9d9bd8accf97"] }, Open ]], Cell[5561, 199, 993, 25, 93, "Text",ExpressionUUID->"447c094b-2493-42bb-94e0-a01c4eede6ac"], Cell[6557, 226, 153, 3, 51, "Output",ExpressionUUID->"1666efba-610e-4536-a02c-5229e2b59d39"], Cell[6713, 231, 285, 5, 45, "Input",ExpressionUUID->"2d80a300-14ab-44c2-be1a-24c3c9515f39"], Cell[7001, 238, 154, 3, 45, "Input",ExpressionUUID->"ad214f94-4531-4380-ba5f-c2ae41e6f8fe"], Cell[7158, 243, 285, 5, 45, "Input",ExpressionUUID->"51fe52ff-e512-417e-813d-8762a79cf229"], Cell[7446, 250, 156, 3, 45, "Input",ExpressionUUID->"0ff394c9-e76e-483b-be35-6ad51b963f8e"], Cell[7605, 255, 437, 7, 45, "Input",ExpressionUUID->"d451e8dc-c133-4b59-8935-8f1177c510aa"], Cell[8045, 264, 149, 3, 76, "Input",ExpressionUUID->"57612376-b42c-40d5-8de1-9023a91f614b"], Cell[8197, 269, 187, 4, 55, "Text",ExpressionUUID->"ac73dec3-6884-4aa0-8990-b33854f00cb7"], Cell[8387, 275, 151, 3, 45, "Input",ExpressionUUID->"243547ad-639d-493f-9033-27f62c83fcea"], Cell[CellGroupData[{ Cell[8563, 282, 472, 10, 93, "Input",ExpressionUUID->"a5cd3a9b-4c6a-4a12-a6fc-db27d0b1642f"], Cell[9038, 294, 403, 10, 51, "Output",ExpressionUUID->"a8969f12-1e30-4868-8844-c678031e4322"] }, Open ]], Cell[CellGroupData[{ Cell[9478, 309, 383, 9, 93, "Input",ExpressionUUID->"3e01a96e-99ca-4740-873a-c3954edd737e"], Cell[9864, 320, 403, 10, 51, "Output",ExpressionUUID->"ceded3cc-02ce-4b1c-896f-28fc5b594962"] }, Open ]], Cell[CellGroupData[{ Cell[10304, 335, 277, 5, 45, "Input",ExpressionUUID->"5e904637-5b7a-4a8f-b254-634c36df03a3"], Cell[10584, 342, 788, 22, 119, "Output",ExpressionUUID->"193adc2f-5c87-4491-9e62-6dbbccde3da4"] }, Open ]], Cell[11387, 367, 282, 5, 45, "Input",ExpressionUUID->"fed3e554-b1af-4902-afe6-356f7f3f29bd"], Cell[11672, 374, 750, 21, 93, "Input",ExpressionUUID->"70692a0a-6668-4bea-84c9-6ec01064ab16"], Cell[12425, 397, 187, 4, 55, "Text",ExpressionUUID->"7eb3a044-02f9-4ae1-9b9c-115b3e265e45"], Cell[12615, 403, 358, 8, 45, "Input",ExpressionUUID->"16729cba-3ae2-4b0e-b9aa-71f725a2495f"], Cell[CellGroupData[{ Cell[12998, 415, 458, 11, 45, "Input",ExpressionUUID->"e0ee5f99-2352-466f-b5bc-ae808dc8a7d9"], Cell[13459, 428, 813, 22, 119, "Output",ExpressionUUID->"05482d83-4fae-4512-8aa2-2d92abc551a5"] }, Open ]], Cell[CellGroupData[{ Cell[14309, 455, 843, 21, 93, "Input",ExpressionUUID->"4ffc188b-efa7-4770-842a-e7c45e63e73e"], Cell[15155, 478, 446, 11, 51, "Output",ExpressionUUID->"6a4ac5ed-2eea-42a0-bf78-89197f1b89ea"] }, Open ]], Cell[15616, 492, 244, 4, 45, "Input",ExpressionUUID->"8c23beee-6d62-4a10-9cec-d06d8d2b2dca"], Cell[15863, 498, 1099, 31, 180, "Text",ExpressionUUID->"4bc2063b-627b-4b61-a044-18e30178905f"], Cell[CellGroupData[{ Cell[16987, 533, 1054, 29, 138, "Input",ExpressionUUID->"5d020818-6975-4e9d-a8ac-af8ffc73c6d7"], Cell[18044, 564, 669, 18, 71, "Output",ExpressionUUID->"44426ac1-d6ea-4478-bece-c1419d6cc83c"] }, Open ]], Cell[18728, 585, 331, 5, 45, "Input",ExpressionUUID->"953d706d-4d5c-45f0-90b8-14f393c92a0f"], Cell[19062, 592, 162, 2, 55, "Text",ExpressionUUID->"e7a4ab07-7faf-4da6-af05-56593ea1f819"], Cell[19227, 596, 153, 6, 91, "Text",ExpressionUUID->"5f219e44-489e-4b34-980a-c6db65a16cb3"], Cell[19383, 604, 364, 9, 76, "Input",ExpressionUUID->"8bd178d6-fa9b-432b-aab7-743b9a47a7f6"], Cell[19750, 615, 422, 9, 45, "Input",ExpressionUUID->"cd4cc325-2c1a-4592-8800-6c1bf822e7ea"], Cell[20175, 626, 348, 10, 45, "Input",ExpressionUUID->"77956d4b-70b7-4ea7-a626-bf0f0e4f0ecb"], Cell[20526, 638, 307, 4, 55, "Text",ExpressionUUID->"eb9aa09c-9cde-440b-aa39-6a6eacdcf2af"], Cell[CellGroupData[{ Cell[20858, 646, 356, 8, 45, "Input",ExpressionUUID->"7b2b2f0d-545a-413e-bd5c-71e90fc8e05b"], Cell[21217, 656, 293, 8, 51, "Output",ExpressionUUID->"140d6718-7c30-4129-9ab4-58818c1dbf74"] }, Open ]], Cell[21525, 667, 296, 4, 55, "Text",ExpressionUUID->"c24646a9-fc7d-4625-8cd4-37b09c27ae4f"], Cell[CellGroupData[{ Cell[21846, 675, 300, 6, 45, "Input",ExpressionUUID->"ac8388e6-611c-415d-9da8-c51a7c9ba22a"], Cell[22149, 683, 195, 4, 51, "Output",ExpressionUUID->"ba0ff84f-5ff7-4a1d-8bb6-e86e62ce5e25"] }, Open ]], Cell[CellGroupData[{ Cell[22381, 692, 451, 12, 76, "Input",ExpressionUUID->"227ae1e2-b199-4abb-a169-0f442d759d22"], Cell[22835, 706, 316, 8, 51, "Output",ExpressionUUID->"f6f8b34d-fcc0-4012-aa25-a0b6d487dc38"] }, Open ]], Cell[23166, 717, 154, 3, 45, "Input",ExpressionUUID->"1b67ae46-7155-4f7d-8f8d-385480723f5f"], Cell[CellGroupData[{ Cell[23345, 724, 353, 9, 45, "Input",ExpressionUUID->"da1e2687-ff22-46d0-86f7-1158aa74b497"], Cell[23701, 735, 316, 8, 51, "Output",ExpressionUUID->"e840fdb5-bcc7-4ecb-ad2d-dcf81b252ee2"] }, Open ]], Cell[CellGroupData[{ Cell[24054, 748, 253, 5, 45, "Input",ExpressionUUID->"c1e8b51b-a419-487f-a44c-42eea33617fa"], Cell[24310, 755, 218, 4, 51, "Output",ExpressionUUID->"cb0b7fa7-28e2-4f06-9566-c9a08c16abf6"] }, Open ]], Cell[24543, 762, 156, 3, 45, "Input",ExpressionUUID->"d3b4949f-9414-491f-8890-7d7420c034ea"], Cell[24702, 767, 174, 4, 140, "Text",ExpressionUUID->"fec6b82a-950c-43ae-85c7-11baec217615"], Cell[CellGroupData[{ Cell[24901, 775, 1800, 40, 424, "Input",ExpressionUUID->"d7d2a6b4-ac56-4d38-8cb5-81b1361d209a"], Cell[26704, 817, 475, 11, 1838, "Output",ExpressionUUID->"8511e14d-99ae-4439-88c6-56b4dbdfe087"] }, Open ]], Cell[27194, 831, 146, 3, 140, "Text",ExpressionUUID->"866937b1-f16b-4554-b708-1b29c24eb42d"], Cell[CellGroupData[{ Cell[27365, 838, 1217, 32, 424, "Input",ExpressionUUID->"daf3b5bd-9f55-4b69-9010-4bf264c1bfd6"], Cell[28585, 872, 447, 10, 1838, "Output",ExpressionUUID->"312a533e-3a4f-4473-b928-d5c2e23a78e0"] }, Open ]], Cell[29047, 885, 146, 3, 140, "Text",ExpressionUUID->"c7fb965f-9299-4363-8e55-ed77d0a5b56d"], Cell[CellGroupData[{ Cell[29218, 892, 363, 6, 115, "Input",ExpressionUUID->"de5b972d-df5b-4698-857b-d0b569b5fe98"], Cell[29584, 900, 314, 8, 181, "Output",ExpressionUUID->"3024182b-c2a4-4156-b5a3-dc9b2778c49c"] }, Open ]], Cell[CellGroupData[{ Cell[29935, 913, 239, 4, 115, "Input",ExpressionUUID->"43d87f25-60bb-4470-87b5-3272e8ae478d"], Cell[30177, 919, 237, 5, 130, "Output",ExpressionUUID->"9483113f-ba8b-4ec7-b38a-927961c5d026"] }, Open ]], Cell[CellGroupData[{ Cell[30451, 929, 415, 9, 184, "Input",ExpressionUUID->"688da978-cdf4-46bb-9718-36f5bd70d6d3"], Cell[30869, 940, 356, 8, 181, "Output",ExpressionUUID->"e5bdb38e-d5f8-49e2-8dad-2dd096b26e4f"] }, Open ]], Cell[CellGroupData[{ Cell[31262, 953, 389, 8, 115, "Input",ExpressionUUID->"295d4aae-19ef-4389-a690-8a468a81d14e"], Cell[31654, 963, 362, 7, 130, "Output",ExpressionUUID->"3f726b04-a055-4e37-b668-3dc50ff9bf3a"] }, Open ]], Cell[CellGroupData[{ Cell[32053, 975, 2765, 62, 655, "Input",ExpressionUUID->"8218796c-f306-4dad-a44b-f1918a3224f0"], Cell[34821, 1039, 644, 13, 1838, "Output",ExpressionUUID->"5b6e0904-cbee-4c0a-b259-7d315f87bd30"] }, Open ]], Cell[CellGroupData[{ Cell[35502, 1057, 1835, 50, 578, "Input",ExpressionUUID->"78129844-f92e-495e-8bb1-a2ee0a0134f5"], Cell[37340, 1109, 754, 15, 1838, "Output",ExpressionUUID->"e25ce515-9194-4b4c-b196-44405dc2b7cc"] }, Open ]], Cell[38109, 1127, 209, 8, 325, "Text",ExpressionUUID->"f6d00a4c-7269-4512-aeee-10a02becf627"], Cell[38321, 1137, 347, 9, 171, "Input",ExpressionUUID->"a350d63c-6c1a-4e5f-8e4b-7ea8c124efd3"], Cell[38671, 1148, 340, 11, 115, "Input",ExpressionUUID->"074bae88-8745-4d25-bc13-38a850139cc6"], Cell[39014, 1161, 223, 4, 194, "Input",ExpressionUUID->"553e771c-08b1-4886-bc33-67a0dae4d564"], Cell[39240, 1167, 146, 3, 140, "Text",ExpressionUUID->"f7aae6bd-ed36-4577-afd6-9eb57127ffd0"], Cell[CellGroupData[{ Cell[39411, 1174, 1156, 29, 271, "Input",ExpressionUUID->"0f97f007-1aac-4dec-81e2-f41ba5d02954"], Cell[40570, 1205, 689, 16, 1912, "Output",ExpressionUUID->"2b64d38a-717d-45f0-8ec2-112e3fc064e1"] }, Open ]], Cell[CellGroupData[{ Cell[41296, 1226, 2002, 50, 785, "Input",ExpressionUUID->"9b579feb-2366-4204-9af6-081a1487490c"], Cell[43301, 1278, 913, 21, 1822, "Output",ExpressionUUID->"77ced785-f44e-48d2-8a99-1056f5c7ea72"] }, Open ]], Cell[CellGroupData[{ Cell[44251, 1304, 628, 15, 194, "Input",ExpressionUUID->"66eaecf9-b4c5-46bc-966d-d59bacf5f2e6"], Cell[44882, 1321, 537, 18, 238, "Output",ExpressionUUID->"4a48b9df-7931-43ce-9692-12a6254e1f4c"] }, Open ]], Cell[45434, 1342, 154, 3, 115, "Input",ExpressionUUID->"6c460b9b-1851-4647-b941-883b4d4348aa"], Cell[45591, 1347, 205, 4, 115, "Input",ExpressionUUID->"f2bd41d3-9408-42a9-b573-51c287004e3f"], Cell[45799, 1353, 587, 9, 115, "Input",ExpressionUUID->"102e868e-b613-46ba-93bc-18db2f531e0f"], Cell[46389, 1364, 154, 3, 115, "Input",ExpressionUUID->"a3fdd870-bea4-4d49-b2e3-890f16458172"], Cell[46546, 1369, 152, 3, 115, "Input",ExpressionUUID->"ae34e05a-ff1f-458b-9beb-79fbb58a7a49"], Cell[46701, 1374, 150, 3, 115, "Input",ExpressionUUID->"df7deb60-dc2a-4e85-b7ae-3b97c62cecdc"], Cell[46854, 1379, 156, 3, 115, "Input",ExpressionUUID->"c0941a7b-aef1-44d7-9664-5ccd1e465225"], Cell[47013, 1384, 152, 3, 115, "Input",ExpressionUUID->"234e8fcd-ca17-4f42-9f03-b6cd3c849229"], Cell[47168, 1389, 154, 3, 115, "Input",ExpressionUUID->"7de34c32-b1b9-4d80-953e-7fe2bd512b87"], Cell[47325, 1394, 128, 3, 115, "Input",ExpressionUUID->"247e5129-76b1-4bdc-b2ca-b87710d07a8c"] } ] *)