{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Outpu t" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } 1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }} {PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra ce have been redefined and unprotected\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7^r%.BlockDiagonalG%,GramSchmidtG%,JordanBlockG%)LUdecompG%)QRde compG%*WronskianG%'addcolG%'addrowG%$adjG%(adjointG%&angleG%(augmentG% (backsubG%%bandG%&basisG%'bezoutG%,blockmatrixG%(charmatG%)charpolyG%) choleskyG%$colG%'coldimG%)colspaceG%(colspanG%*companionG%'concatG%%co ndG%)copyintoG%*crossprodG%%curlG%)definiteG%(delcolsG%(delrowsG%$detG %%diagG%(divergeG%(dotprodG%*eigenvalsG%,eigenvaluesG%-eigenvectorsG%+ eigenvectsG%,entermatrixG%&equalG%,exponentialG%'extendG%,ffgausselimG %*fibonacciG%+forwardsubG%*frobeniusG%*gausselimG%*gaussjordG%(geneqns G%*genmatrixG%%gradG%)hadamardG%(hermiteG%(hessianG%(hilbertG%+htransp oseG%)ihermiteG%*indexfuncG%*innerprodG%)intbasisG%(inverseG%'ismithG% *issimilarG%'iszeroG%)jacobianG%'jordanG%'kernelG%*laplacianG%*leastsq rsG%)linsolveG%'mataddG%'matrixG%&minorG%(minpolyG%'mulcolG%'mulrowG%) multiplyG%%normG%*normalizeG%*nullspaceG%'orthogG%*permanentG%&pivotG% *potentialG%+randmatrixG%+randvectorG%%rankG%(ratformG%$rowG%'rowdimG% )rowspaceG%(rowspanG%%rrefG%*scalarmulG%-singularvalsG%&smithG%,stackm atrixG%*submatrixG%*subvectorG%)sumbasisG%(swapcolG%(swaprowG%*sylvest erG%)toeplitzG%&traceG%*transposeG%,vandermondeG%*vecpotentG%(vectdimG %'vectorG%*wronskianG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "A: =matrix(4,4,[2,0,0,0,0,2,0,0,0,0,-3,1,0,0,0,-3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7&\"\"#\"\"!F+F+7&F+F*F+F+7&F+F+!\" $\"\"\"7&F+F+F+F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "B:=ran dmatrix(4,4,entries=rand(-2..2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"BG-%'matrixG6#7&7&\"\"!\"\"\"F*!\"#7&F,F,F*F*7&F+F*F*F+7&F*F*F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "A:=evalm(B&*A&*inverse(B) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7&!\")!\"&!# 5\"\"!7&F-\"\"#F-F-7&\"\"&#F1F/\"\"(F-7&F/\"\"\"F/!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "charpoly(A,L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)%\"LG\"\"%\"\"\"F(*&\"\"#F()F&\"\"$F(F(*&\"#6F()F& F*F(!\"\"*&\"#7F(F&F(F0\"#OF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "solve(%,L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&\"\"#F#!\"$F$" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "C:=evalm(A-2*Matrix(4,4,sha pe=identity));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7& 7&!#5!\"&F*\"\"!7&F,F,F,F,7&\"\"&#F/\"\"#F/F,7&F1\"\"\"F1F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "gausselim(C);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"&#F(\"\"#F(\"\"!7&F+F+F+!\"& 7&F+F+F+F+F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "q:=[-1,2,0, 0];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG7&!\"\"\"\"#\"\"!F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(A&*q);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&!\"#\"\"%\"\"!F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "q:=[-1,0,1,0];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG7&!\"\"\"\"!\"\"\"F'" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "evalm(A&*q);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%' vectorG6#7&!\"#\"\"!\"\"#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "C:=evalm(A+3*Matrix(4,4,shape=identity));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7&7&!\"&F*!#5\"\"!7&F,\"\"&F,F,7&F.#F .\"\"#\"#5F,7&F1\"\"\"F1F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "gausselim(C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&! \"&F(!#5\"\"!7&F*\"\"&F*F*7&F*F*!\"#F*7&F*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "q:=[0,0,0,1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG7&\"\"!F&F&\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(A&*q);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&\" \"!F'F'!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "C2:=evalm(C^ 2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#C2G-%'matrixG6#7&7&!#DF*!#] \"\"!7&F,\"#DF,F,7&F.#F.\"\"#\"#]F,7&F,F,F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "gausselim(C2);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#-%'matrixG6#7&7&!#DF(!#]\"\"!7&F*\"#DF*F*7&F*F*F*F*F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "s:=[-2,0,1,0];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG7&!\"#\"\"!\"\"\"F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "q:=evalm(C&*s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"qG-%'vectorG6#7&\"\"!F)F)!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "A:=matrix(4,4,[4 ,1,0,0,0,4,1,0,0,0,4,0,0,0,0,-3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%\"AG-%'matrixG6#7&7&\"\"%\"\"\"\"\"!F,7&F,F*F+F,7&F,F,F*F,7&F,F,F,! \"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "B:=randmatrix(4,4,en tries=rand(-2..2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrix G6#7&7&\"\"#!\"\"\"\"\"!\"#7&F,F+\"\"!F,7&F,F+F,F,7&F,F+F+F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "A:=evalm(B&*A&*inverse(B)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7&\"\"'!#X\"#> \"#A7&\"\"\"\"#5!\"&!\"$7&F/F*!\"\"F27&F/\"#?!#7!\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "charpoly(A,L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)%\"LG\"\"%\"\"\"F(*&\"\"*F()F&\"\"$F(!\"\"*&\"#7F( )F&\"\"#F(F(*&\"#!)F(F&F(F(\"$#>F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "solve(%,L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&!\"$\" \"%F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "C:=evalm(A+3*Mat rix(4,4,shape=identity));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%' matrixG6#7&7&\"\"*!#X\"#>\"#A7&\"\"\"\"#8!\"&!\"$7&F/\"\"'\"\"#F27&F/ \"#?!#7F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "gausselim(C); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"*!#X\"#>\"#A7& \"\"!\"#=#!#kF(#!#\\F(7&F-F-#\"$V$\"#\")#!$V$\"$i\"7&F-F-F-F-" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "q:=[-2,1,1,2];" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"qG7&!\"#\"\"\"F'\"\"#" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 12 "evalm(A&*q);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#-%'vectorG6#7&\"\"'!\"$F(!\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "C:=evalm(A-4*Matrix(4,4,shape=identity));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7&7&\"\"#!#X\"#>\"#A7&\"\"\"\"\"'!\"& !\"$F.7&F/\"#?!#7!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "gau sselim(C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"#!#X \"#>\"#A7&\"\"!#\"#dF(#!#HF(!#97&F-F-#\"\"(F/#!\"(F/7&F-F-F-F-" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "q:=[2,1,1,1];" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"qG7&\"\"#\"\"\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(A&*q);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# -%'vectorG6#7&\"\")\"\"%F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "C2:=evalm(C^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#C2G-%'matr ixG6#7&7&\"\"!\"$%>!#'*!#)*7&F*!#**\"#]\"#\\F.7&F*!$(>\"#**\"#)*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "gausselim(C2);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"!!#**\"#]\"#\\7&F(F(#!#\\\"# **#F+F/7&F(F(F(F(F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "s:=[ 1,0,0,0]; # or [0,1,1,1]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG7&\" \"\"\"\"!F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "q:=evalm(C &*s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG-%'vectorG6#7&\"\"#\"\" \"F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "C3:=evalm(C^3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#C3G-%'matrixG6#7&7&\"\"!!%s8\"$'o F,7&F*F,!$V$F.F-7&F*\"%s8!$'oF1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "gausselim(C3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6# 7&7&\"\"!\"$'o!$V$F*7&F(F(F(F(F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "u:=[0,1,2,0]; # or [0,1,0,2] but not [1,0,0,0]" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG7&\"\"!\"\"\"\"\"#F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "s:=evalm(C&*u);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"sG-%'vectorG6#7&!\"(!\"%F*F*" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 15 "q:=evalm(C&*s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG-%'vectorG6#7&\"\"#\"\"\"F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 49 "A:=evalm(randmatrix(5,5,entries=rand(-2..2)) *1.);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7'7'$!\"\" \"\"!$\"\"#F,F-$!\"#F,F/7'$F,F,F-F2F-F*7'F2F/F-F/F*7'F2$\"\"\"F,F*F*F2 7'F*F5F/F2F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "U:=Matrix(5 ,5,shape=identity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"UG-%'RTABLE G6%\")78V7-%'MATRIXG6#7'7'\"\"\"\"\"!F/F/F/7'F/F.F/F/F/7'F/F/F.F/F/7'F /F/F/F.F/7'F/F/F/F/F.%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "det(U*lambda-A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.*$)%'lam bdaG\"\"&\"\"\"F(*&$\"\"#\"\"!F()F&\"\"%F(!\"\"*&$\"#5F,F()F&\"\"$F(F/ *&$F2F,F()F&F+F(F(*&$\"#RF,F(F&F(F($\"#EF,F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "cp:=charpoly(A,lambda);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#cpG,.*$)%'lambdaG\"\"&\"\"\"F**&$\"\"#\"\"!F*)F(\"\" %F*!\"\"*&$\"#5F.F*)F(\"\"$F*F1*&$F4F.F*)F(F-F*F**&$\"#RF.F*F(F*F*$\"# EF.F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "trace(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "det(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!#E\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "aux:=0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "for i to 4 do for j from i+1 to 5 do aux: =aux+det(submatrix(A,[i,j],[i,j])) end do end do;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 4 "aux;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!#5 \"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "eva:=fsolve(cp,lam bda,complex);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$evaG6'$!+b#\\\"G@! \"*^$$!+(*RG45F($!+8Vu]X!#5^$F*$\"+8Vu]XF.^$$\"+D'eL2$F($!+3z@AsF.^$F3 $\"+3z@AsF." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "eigenvals(A) ;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6'^$$\"+D'eL2$!\"*$\"+3z@As!#5^$F$$ !+3z@AsF)^$$!+(*RG45F&$\"+8Vu]XF)^$F.$!+8Vu]XF)$!+b#\\\"G@F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eigenvects(A);" }}{PARA 12 " " 1 "" {XPPMATH 20 "6'7%^$$\"+D'eL2$!\"*$\"+ry@As!#5\"\"\"<#-%'vectorG 6#7'^$$\"+i*G')R\"F'$\"+o7(R9%F*^$$\"+gC;6[F*$!+GRnQHF*^$$\"+#*y$R%)*F *$\"+'f/ca)F*^$$!+1a_#o\"F*$!+'RX5_#F*^$$!+'y_^1\"F'$!+Ehci`F*7%^$F%$! +ry@AsF*F+<#-F.6#7'^$F2$!+o7(R9%F*^$F7$\"+GRnQHF*^$F<$!+'f/ca)F*^$FA$ \"+'RX5_#F*^$FF$\"+Ehci`F*7%^$$!++SG45F'$\"+)HW2b%F*F+<#-F.6#7'^$$!+c[ *R$QF*$!+#H&Ro!*F*^$$\"+GbU.JF*$!+Iv6BWF*^$$\"+M-mmTF*$!+%ptq2%F*^$$!+ +2]Cr!#6$\"+o?$4N#F*^$$\"+J5M,fF*$!+BU3-5F'7%^$F]o$!+)HW2b%F*F+<#-F.6# 7'^$Ffo$\"+#H&Ro!*F*^$F[p$\"+Iv6BWF*^$F`p$\"+%ptq2%F*^$Fep$!+o?$4N#F*^ $F[q$\"+BU3-5F'7%$!+_#\\\"G@F'F+<#-F.6#7'$\"+mVHJ@F'$\"+TiRO:F*$\"+YHS 6oF*$\"+tc!en%F*$\"+6%3%p:F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evalm((A-eva[5])^2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-%'matri xG6#7'7'^$$\"+\"F+$\"+SJHRWF." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "linsolve(A,randvector(5,entr ies=rand(-3..3)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7'$! +xI#p2#!\"*$\"+YQ:Y=F)$\"+i%Q:'>F)$!+bh%Q:\"!#5$\"+i%Q:Y$F)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "A:=randmatrix(6,8,entries=ra nd(0..1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7(7*\" \"!\"\"\"F*F+F*F*F+F+7*F*F+F+F*F*F+F+F*7*F+F+F+F+F+F+F*F+7*F*F*F+F*F*F +F+F*7*F*F*F+F+F*F*F+F+7*F*F*F*F+F+F*F*F*" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 13 "gausselim(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-% 'matrixG6#7(7*\"\"\"F(F(F(F(F(\"\"!F(7*F)F(F(F)F)F(F(F)7*F)F)!\"\"F(F) F,F)F(7*F)F)F)F(F)F)F(F(7*F)F)F)F)F(F)F,F,7*F)F)F)F)F)F,F,F)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "linsolve(A,randvector(6,entr ies=rand(-2..2)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7*,( \"\"\"!\"\"&%#_tG6#\"\"#F)*&F-F(&F+6#F(F(F)F-\"\"$F*,&F*F)F(F(,(\"\"%F )F*F(F/F(,(F(F)F*F)F/F)F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "A:=randmatrix(3,3,entries=rand(-3..3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%\"\"#!\"#!\"\"7%\"\"!\"\"$F/7%F+F ,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "yv:=[seq(y[i](x),i=1 ..3)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#yvG7%-&%\"yG6#\"\"\"6#%\" xG-&F(6#\"\"#F+-&F(6#\"\"$F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "aux:=evalm(A&*yv);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$auxG-%' vectorG6#7%,(*&\"\"#\"\"\"-&%\"yG6#F,6#%\"xGF,F,*&F+F,-&F/6#F+F1F,!\" \"-&F/6#\"\"$F1F7,&*&F;F,F4F,F,*&F;F,F8F,F,,(*&F+F,F-F,F7F4F7*&F+F,F8F ,F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "eq:=\{seq(diff(y[i]( x),x)=aux[i],i=1..3)\};" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#eqG<%/-% %diffG6$-&%\"yG6#\"\"\"6#%\"xGF0,(*&\"\"#F.F*F.F.*&F3F.-&F,6#F3F/F.!\" \"-&F,6#\"\"$F/F8/-F(6$F5F0,&*&F " 0 "" {MPLTEXT 1 0 11 " dsolve(eq);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<%/-&%\"yG6#\"\"$6#%\"x G,,*&#\"\"\"\"\"#F/*&%$_C2GF/-%$expG6#*&,&#F)F0F/*&F0!\"\"\"#@#F/F0F/F /F+F/F/F/F:*&#F/\"\"'F/*(F2F/F3F/F;FF/FLF/F/*&F0F:FM F/F//-&F'6#F0F*,(FMF/F1F/FCF/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "45 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 12431312 }{RTABLE M7R0 I5RTABLE_SAVE/12431312X,%)anythingG6#%)identityG6"[gl!""!!!#!"&"&6" }