%% Created by Maple 18.01, Windows 8
%% Source Worksheet: Example1.mw
%% Generated: Sun Nov 01 18:12:57 IRST 2015
\documentclass{article}
\usepackage{maplestd2e}
\def\emptyline{\vspace{12pt}}
\begin{document}
\pagestyle{empty}
\DefineParaStyle{Maple Heading 1}
\DefineParaStyle{Maple Text Output}
\DefineParaStyle{Maple Dash Item}
\DefineParaStyle{Maple Bullet Item}
\DefineParaStyle{Maple Normal}
\DefineParaStyle{Maple Heading 4}
\DefineParaStyle{Maple Heading 3}
\DefineParaStyle{Maple Heading 2}
\DefineParaStyle{Maple Warning}
\DefineParaStyle{Maple Title}
\DefineParaStyle{Maple Error}
\DefineCharStyle{Maple Hyperlink}
\DefineCharStyle{Maple 2D Math}
\DefineCharStyle{Maple Maple Input}
\DefineCharStyle{Maple 2D Output}
\DefineCharStyle{Maple 2D Input}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{with(LinearAlgebra); 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{[`&x`, Add, Adjoint, BackwardSubstitute, BandMatrix, Basis, BezoutMatrix, BidiagonalForm, BilinearForm, CARE, CharacteristicMatrix, CharacteristicPolynomial, Column, ColumnDimension, ColumnOperation, ColumnSpace, CompanionMatrix, CompressedSparseForm, ConditionNumber, ConstantMatrix, ConstantVector, Copy, CreatePermutation, CrossProduct, DARE, DeleteColumn, DeleteRow, Determinant, Diagonal, DiagonalMatrix, Dimension, Dimensions, DotProduct, EigenConditionNumbers, Eigenvalues, Eigenvectors, Equal, ForwardSubstitute, FrobeniusForm, FromCompressedSparseForm, FromSplitForm, GaussianElimination, GenerateEquations, GenerateMatrix, Generic, GetResultDataType, GetResultShape, GivensRotationMatrix, GramSchmidt, HankelMatrix, HermiteForm, HermitianTranspose, HessenbergForm, HilbertMatrix, HouseholderMatrix, IdentityMatrix, IntersectionBasis, IsDefinite, IsOrthogonal, IsSimilar, IsUnitary, JordanBlockMatrix, JordanForm, KroneckerProduct, LA_Main, LUDecomposition, LeastSquares, LinearSolve, LyapunovSolve, Map, Map2, MatrixAdd, MatrixExponential, MatrixFunction, MatrixInverse, MatrixMatrixMultiply, MatrixNorm, MatrixPower, MatrixScalarMultiply, MatrixVectorMultiply, MinimalPolynomial, Minor, Modular, Multiply, NoUserValue, Norm, Normalize, NullSpace, OuterProductMatrix, Permanent, Pivot, PopovForm, ProjectionMatrix, QRDecomposition, RandomMatrix, RandomVector, Rank, RationalCanonicalForm, ReducedRowEchelonForm, Row, RowDimension, RowOperation, RowSpace, ScalarMatrix, ScalarMultiply, ScalarVector, SchurForm, SingularValues, SmithForm, SplitForm, StronglyConnectedBlocks, SubMatrix, SubVector, SumBasis, SylvesterMatrix, SylvesterSolve, ToeplitzMatrix, Trace, Transpose, TridiagonalForm, UnitVector, VandermondeMatrix, VectorAdd, VectorAngle, VectorMatrixMultiply, VectorNorm, VectorScalarMultiply, ZeroMatrix, ZeroVector, Zip]}{\[\displaystyle [\mbox {{\tt `\&x`}},{\it Add},{\it Adjoint},{\it BackwardSubstitute}\\
\mbox{},{\it BandMatrix},{\it Basis},{\it BezoutMatrix},{\it BidiagonalForm}\\
\mbox{},{\it BilinearForm},{\it CARE},{\it CharacteristicMatrix}\\
\mbox{},{\it CharacteristicPolynomial},{\it Column},{\it ColumnDimension}\\
\mbox{},{\it ColumnOperation},{\it ColumnSpace},{\it CompanionMatrix}\\
\mbox{},{\it CompressedSparseForm},{\it ConditionNumber}\\
\mbox{},{\it ConstantMatrix},{\it ConstantVector},{\it Copy}\\
\mbox{},{\it CreatePermutation},{\it CrossProduct},{\it DARE}\\
\mbox{},{\it DeleteColumn},{\it DeleteRow},{\it Determinant}\\
\mbox{},{\it Diagonal},{\it DiagonalMatrix},{\it Dimension}\\
\mbox{},{\it Dimensions},{\it DotProduct},{\it EigenConditionNumbers}\\
\mbox{},{\it Eigenvalues},{\it Eigenvectors},{\it Equal}\\
\mbox{},{\it ForwardSubstitute},{\it FrobeniusForm},{\it FromCompressedSparseForm}\\
\mbox{},{\it FromSplitForm},{\it GaussianElimination},{\it GenerateEquations}\\
\mbox{},{\it GenerateMatrix},{\it Generic},{\it GetResultDataType}\\
\mbox{},{\it GetResultShape},{\it GivensRotationMatrix},{\it GramSchmidt}\\
\mbox{},{\it HankelMatrix},{\it HermiteForm},{\it HermitianTranspose}\\
\mbox{},{\it HessenbergForm},{\it HilbertMatrix},{\it HouseholderMatrix}\\
\mbox{},{\it IdentityMatrix},{\it IntersectionBasis},{\it IsDefinite}\\
\mbox{},{\it IsOrthogonal},{\it IsSimilar},{\it IsUnitary}\\
\mbox{},{\it JordanBlockMatrix},{\it JordanForm},{\it KroneckerProduct}\\
\mbox{},{\it LA\_Main},{\it LUDecomposition},{\it LeastSquares}\\
\mbox{},{\it LinearSolve},{\it LyapunovSolve},{\it Map},{\it Map2}\\
\mbox{},{\it MatrixAdd},{\it MatrixExponential},{\it MatrixFunction}\\
\mbox{},{\it MatrixInverse},{\it MatrixMatrixMultiply},{\it MatrixNorm}\\
\mbox{},{\it MatrixPower},{\it MatrixScalarMultiply},{\it MatrixVectorMultiply}\\
\mbox{},{\it MinimalPolynomial},{\it Minor},{\it Modular}\\
\mbox{},{\it Multiply},{\it NoUserValue},{\it Norm},{\it Normalize}\\
\mbox{},{\it NullSpace},{\it OuterProductMatrix},{\it Permanent}\\
\mbox{},{\it Pivot},{\it PopovForm},{\it ProjectionMatrix}\\
\mbox{},{\it QRDecomposition},{\it RandomMatrix},{\it RandomVector}\\
\mbox{},{\it Rank},{\it RationalCanonicalForm},{\it ReducedRowEchelonForm}\\
\mbox{},{\it Row},{\it RowDimension},{\it RowOperation},{\it RowSpace}\\
\mbox{},{\it ScalarMatrix},{\it ScalarMultiply},{\it ScalarVector}\\
\mbox{},{\it SchurForm},{\it SingularValues},{\it SmithForm}\\
\mbox{},{\it SplitForm},{\it StronglyConnectedBlocks},{\it SubMatrix}\\
\mbox{},{\it SubVector},{\it SumBasis},{\it SylvesterMatrix}\\
\mbox{},{\it SylvesterSolve},{\it ToeplitzMatrix},{\it Trace}\\
\mbox{},{\it Transpose},{\it TridiagonalForm},{\it UnitVector}\\
\mbox{},{\it VandermondeMatrix},{\it VectorAdd},{\it VectorAngle}\\
\mbox{},{\it VectorMatrixMultiply},{\it VectorNorm},{\it VectorScalarMultiply}\\
\mbox{},{\it ZeroMatrix},{\it ZeroVector},{\it Zip}]\]}
\end{maplelatex}
\end{maplegroup}
\mapleinline{inert}{2d}{}{\[\displaystyle \]}
\mapleinline{inert}{2d}{}{\[\displaystyle \]}
\mapleinline{inert}{2d}{}{\[\displaystyle \]}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{N := 3; 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{N := 3}{\[\displaystyle N\, := \,3\]}
\end{maplelatex}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\mapleinline{inert}{2d}{}{\[\displaystyle \]}
\mapleinline{inert}{2d}{}{\[\displaystyle \]}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{h := proc (i, j) options operator, arrow; piecewise(j = 1, 1, j = 2, (2*i-2)/N, j = 3, 4*(i-1)^2/N^2-2, j = 4, 8*(i-1)^3/N^3-12*(i-1)/N, j = 5, 16*(i-1)^4/N^4-48*(i-1)^2/N^2+12, j = 6, 32*(i-1)^5/N^5-160*(i-1)^3/N^3+120*(i-1)/N, j = 7, 64*(i-1)^6/N^6-480*(i-1)^4/N^4+720*(i-1)^2/N^2-120, j = 8, 128*(i-1)^7/N^7-1344*(i-1)^5/N^5+3360*(i-1)^3/N^3-1680*(i-1)/N, j = 9, 256*(i-1)^8/N^8-3584*(i-1)^6/N^6+13440*(i-1)^4/N^4-13440*(i-1)^2/N^2+1680, j = 10, 512*(i-1)^9/N^9-9216*(i-1)^7/N^7+4838*(i-1)^5/N^5-80640*(i-1)^3/N^3+30240*(i-1)/N, j = 11, 1024*(i-1)^10/N^10-23040*(i-1)^8/N^8+161280*(i-1)^6/N^6-403200*(i-1)^4/N^4+302400*(i-1)^2/N^2-30240) end proc; -1; H := Matrix(N+1, N+1, h); 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{H := Matrix(%id = 18446744074226256342)}{\[\displaystyle H\, := \, \left[ \begin {array}{cccc} 1&0&-2&0\\ \noalign{\medskip}1&2/3&-{\frac {14}{9}}&-{\frac {100}{27}}\\ \noalign{\medskip}1&4/3&-2/9&-{\frac {152}{27}}\\ \noalign{\medskip}1&2&2&-4\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{k := proc (i, j) options operator, arrow; piecewise(j = 1, 1, j = 2, (1/2)*(2*i-2)/N, j = 3, (i-1)^2/N^2-2, j = 4, (i-1)^3/N^3-6*(i-1)/N) end proc; -1; K := Matrix(N+1, N+1, k); 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{K := Matrix(%id = 18446744074226247310)}{\[\displaystyle K\, := \, \left[ \begin {array}{cccc} 1&0&-2&0\\ \noalign{\medskip}1&1/3&-{\frac {17}{9}}&-{\frac {53}{27}}\\ \noalign{\medskip}1&2/3&-{\frac {14}{9}}&-{\frac {100}{27}}\\ \noalign{\medskip}1&1&-1&-5\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{m := proc (i, j) options operator, arrow; piecewise(i = N+1, 0, i+1 = j, 2*j-2) end proc; -1; M[Transpose] := Matrix(N+1, N+1, m); 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{M[`LinearAlgebra:-Transpose`] := Matrix(%id = 18446744074226248150)}{\[\displaystyle M_{{\mbox {{\tt `LinearAlgebra:-Transpose`}}}}\, := \, \left[ \begin {array}{cccc} 0&2&0&0\\ \noalign{\medskip}0&0&4&0\\ \noalign{\medskip}0&0&0&6\\ \noalign{\medskip}0&0&0&0\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\mapleinline{inert}{2d}{g := proc (i, j) options operator, arrow; -(i-1)^2/N^2+2 end proc; -1}{\[\displaystyle \]}
\mapleinline{inert}{2d}{G := Matrix(N+1, 1, g); 1}{\[\displaystyle \]}
\begin{maplegroup}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Matrix(%id = 18446744074226248630)}{\[\displaystyle  \left[ \begin {array}{c} 2\\ \noalign{\medskip}{\frac {17}{9}}\\ \noalign{\medskip}{\frac {14}{9}}\\ \noalign{\medskip}1\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\mapleinline{inert}{2d}{}{\[\displaystyle \]}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{p := proc (i, j) options operator, arrow; piecewise(i = j, 1) end proc; -1; P(1) := Matrix(N+1, N+1, p); 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{P(1) := Matrix(%id = 18446744074226249110)}{\[\displaystyle P \left( 1 \right) \, := \, \left[ \begin {array}{cccc} 1&0&0&0\\ \noalign{\medskip}0&1&0&0\\ \noalign{\medskip}0&0&1&0\\ \noalign{\medskip}0&0&0&1\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{p := proc (i, j) options operator, arrow; piecewise(i = j, 3/4) end proc; -1; P(0) := Matrix(N+1, N+1, p); 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{P(0) := Matrix(%id = 18446744074226241534)}{\[\displaystyle P \left( 0 \right) \, := \, \left[ \begin {array}{cccc} 3/4&0&0&0\\ \noalign{\medskip}0&3/4&0&0\\ \noalign{\medskip}0&0&3/4&0\\ \noalign{\medskip}0&0&0&3/4\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{W := Multiply(H, M[Transpose]^2)-Multiply(P(0), H)-Multiply(P(1), K); 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{W := Matrix(%id = 18446744074226243454)}{\[\displaystyle W\, := \, \left[ \begin {array}{cccc} -7/4&0&23/2&0\\ \noalign{\medskip}-7/4&-5/6&{\frac {199}{18}}&{\frac {560}{27}}\\ \noalign{\medskip}-7/4&-5/3&{\frac {175}{18}}&{\frac {1078}{27}}\\ \noalign{\medskip}-7/4&-5/2&15/2&56\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{S := Matrix([W, G]); 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{S := Matrix(%id = 18446744074226243694)}{\[\displaystyle S\, := \, \left[ \begin {array}{ccccc} -7/4&0&23/2&0&2\\ \noalign{\medskip}-7/4&-5/6&{\frac {199}{18}}&{\frac {560}{27}}&{\frac {17}{9}}\\ \noalign{\medskip}-7/4&-5/3&{\frac {175}{18}}&{\frac {1078}{27}}&{\frac {14}{9}}\\ \noalign{\medskip}-7/4&-5/2&15/2&56&1\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{U[0] := Multiply(H, M[Transpose]^0); 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{U[0] := Matrix(%id = 18446744074226244054)}{\[\displaystyle U_{{0}}\, := \, \left[ \begin {array}{cccc} 1&0&-2&0\\ \noalign{\medskip}1&2/3&-{\frac {14}{9}}&-{\frac {100}{27}}\\ \noalign{\medskip}1&4/3&-2/9&-{\frac {152}{27}}\\ \noalign{\medskip}1&2&2&-4\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{U[0][1, 1 .. N+1]; 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Vector[row](%id = 18446744074226244294)}{\[\displaystyle  \left[ \begin {array}{cccc} 1&0&-2&0\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{U[1] := Multiply(H, M[Transpose]); 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{U[1] := Matrix(%id = 18446744074226244654)}{\[\displaystyle U_{{1}}\, := \, \left[ \begin {array}{cccc} 0&2&0&-12\\ \noalign{\medskip}0&2&8/3&-{\frac {28}{3}}\\ \noalign{\medskip}0&2&16/3&-4/3\\ \noalign{\medskip}0&2&8&12\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{U[1][1, 1 .. N+1]; 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Vector[row](%id = 18446744074226244894)}{\[\displaystyle  \left[ \begin {array}{cccc} 0&2&0&-12\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{V := Matrix([[W[1, 1 .. N+1]], [U[0][1, 1 .. N+1]], [U[1][1, 1 .. N+1]], [W[N+1, 1 .. N+1]]]); 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{V := Matrix(%id = 18446744074226245254)}{\[\displaystyle V\, := \, \left[ \begin {array}{cccc} -7/4&0&23/2&0\\ \noalign{\medskip}1&0&-2&0\\ \noalign{\medskip}0&2&0&-12\\ \noalign{\medskip}-7/4&-5/2&15/2&56\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\mapleinline{inert}{2d}{q := proc (i, j) options operator, arrow; piecewise(i = 1, -(i-1)^2/N^2+2, i = 2, 0, i = 3, 0, i = 4, -(i-1)^2/N^2+2) end proc; -1}{\[\displaystyle \]}
\mapleinline{inert}{2d}{Q := Matrix(N+1, 1, q); 1}{\[\displaystyle \]}
\begin{maplegroup}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Matrix(%id = 18446744074226237798)}{\[\displaystyle  \left[ \begin {array}{c} 2\\ \noalign{\medskip}0\\ \noalign{\medskip}0\\ \noalign{\medskip}1\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\mapleinline{inert}{2d}{}{\[\displaystyle \]}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{L := Matrix([V, Q]); 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{L := Matrix(%id = 18446744074226237918)}{\[\displaystyle L\, := \, \left[ \begin {array}{ccccc} -7/4&0&23/2&0&2\\ \noalign{\medskip}1&0&-2&0&0\\ \noalign{\medskip}0&2&0&-12&0\\ \noalign{\medskip}-7/4&-5/2&15/2&56&1\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{Y := MatrixInverse(V); 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{Y := Matrix(%id = 18446744074226238278)}{\[\displaystyle Y\, := \, \left[ \begin {array}{cccc} 1/4&{\frac {23}{16}}&0&0\\ \noalign{\medskip}-{\frac {3}{41}}&{\frac {21}{164}}&{\frac {28}{41}}&{\frac {6}{41}}\\ \noalign{\medskip}1/8&{\frac {7}{32}}&0&0\\ \noalign{\medskip}-{\frac {1}{82}}&{\frac {7}{328}}&{\frac {5}{164}}&1/41\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{A := evalm(`&*`(Y, Q)); 1}{\[\]}
\end{mapleinput}
\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{A := Vector[column](%id = 18446744074226238518)}{\[\displaystyle A\, := \, \left[ \begin {array}{c} 1/2\\ \noalign{\medskip}0\\ \noalign{\medskip}1/4\\ \noalign{\medskip}0\end {array} \right] \]}
\end{maplelatex}
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{2d}{}{\[\]}
\end{mapleinput}
\end{maplegroup}
\end{document}