{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 } {CSTYLE "" -1 256 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE " Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE " " -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "Example 1." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "x[-1] := x[0]-h:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "x[1] := x[0] + h: x[2] := x[0]+2*h:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 215 "for k from 0 to 3 do\n f := (t-x [0])^k:\n eq[k] := subs(t=x[0],diff(f,t$2)) = a*subs(t=x[-1],f) + \n b*subs(t=x[0],f) + c*subs(t=x[2],diff(f,t)) + \n \+ d*subs(t=x[2],diff(f,t$2)):\nend do:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 44 "for k from 0 to 3 do\n print(eq[k])\nend do; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"!,&%\"aG\"\"\"%\"bGF'" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"!,&*&%\"aG\"\"\"%\"hGF(!\"\"%\"cG F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"#,(*&%\"aG\"\"\")%\"hGF$F(F (*(\"\"%F(%\"cGF(F*F(F(*&F$F(%\"dGF(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"!,(*&%\"aG\"\"\")%\"hG\"\"$F(!\"\"*(\"#7F(%\"cGF()F*\"\"#F( F(*(F.F(%\"dGF(F*F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "so lve(\{seq(eq[k],k=0..3)\},\{a,b,c,d\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&/%\"bG,$*(\"#7\"\"\"\"#>!\"\"%\"hG!\"#F+/%\"dG#!#6F*/%\"cG,$*( F(F)F*F+F,F+F)/%\"aG,$*(F(F)F*F+F,F-F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "Example 2. " }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "for k from 0 to 4 do\n g := t^k:\n eq[k] := int(g,t=0..1) = s[1]*subs (t=u[1],g) + s[2]*subs(t=u[2],g) + s[3]*subs(t=1/2,g):\nend do:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "for k from 0 to 4 do\n pri nt(eq[k])\nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/\"\"\",(&%\"sG6 #F$F$&F'6#\"\"#F$&F'6#\"\"$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/#\" \"\"\"\"#,(*&&%\"sG6#F%F%&%\"uGF+F%F%*&&F*6#F&F%&F-F0F%F%*&F$F%&F*6#\" \"$F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/#\"\"\"\"\"$,(*&&%\"sG6#F% F%)&%\"uGF+\"\"#F%F%*&&F*6#F/F%)&F.F2F/F%F%*&#F%\"\"%F%&F*6#F&F%F%" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/#\"\"\"\"\"%,(*&&%\"sG6#F%F%)&%\"uGF+ \"\"$F%F%*&&F*6#\"\"#F%)&F.F2F/F%F%*&#F%\"\")F%&F*6#F/F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/#\"\"\"\"\"&,(*&&%\"sG6#F%F%)&%\"uGF+\"\"%F %F%*&&F*6#\"\"#F%)&F.F2F/F%F%*&#F%\"#;F%&F*6#\"\"$F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "solve(\{seq(eq[k],k=0..4)\},\{s[1], s[2],s[3],u[1],u[2]\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<'/&%\"sG6# \"\"$#\"\"%\"\"*/&%\"uG6#\"\"#,&-%'RootOfG6#,(*&\"#5\"\"\")%#_ZGF0F8F8 *&F7F8F:F8!\"\"F8F8F " 0 "" {MPLTEXT 1 0 28 "S := solve(10*z^2-10*z+1,z); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG6$,&#\"\"\"\"\"#F(*&\"#5!\" \"\"#:F'F(,&F'F(*&F+F,F-F'F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "-S[2]+1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&#\"\"\"\"\"#F%*&\"# 5!\"\"\"#:F$F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "Review of Linear Algebra" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "E := LinearAlgebr a:-IdentityMatrix(5); # 5x5 identity matrix" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"EG-%'RTABLEG6%\"*ca$p9-%'MATRIXG6#7'7'\"\"\"\"\"!F/ F/F/7'F/F.F/F/F/7'F/F/F.F/F/7'F/F/F/F.F/7'F/F/F/F/F.%'MatrixG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "A := LinearAlgebra:-RandomMa trix(5,5,generator=-9..9);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-% 'RTABLEG6%\"*Kik[\"-%'MATRIXG6#7'7'!\"(!\")\"\"!\"\"&!\"\"7'\"\"#F4F2! \"'!\"&7'!\"*F6!\"$F1!\"%7'\"\"(F4F:F/\"\"\"7'F " 0 "" {MPLTEXT 1 0 70 "# exact LU decomposition\n(P ,L,U) := LinearAlgebra:-LUDecomposition(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6%%\"PG%\"LG%\"UG6%-%'RTABLEG6%\"*_lcZ\"-%'MATRIXG6#7' 7'\"\"\"\"\"!F3F3F37'F3F2F3F3F37'F3F3F2F3F37'F3F3F3F2F37'F3F3F3F3F2%'M atrixG-F*6%\"*wj>Z\"-F.6#7'F17'#!\"#\"\"(F2F3F3F37'#\"\"*FB#!#P\"\"#F2 F3F37'!\"\"\"#@#!#M\"#VF2F37'FJ#\"$>\"FH#!$2\"FN#\"#e\"#DF2F8-F*6%\"*_ \"=)[\"-F.6#7'7'!\"(!\")F3\"\"&FJ7'F3F@FJ#!#KFB#FGFB7'F3F3#!#VFH!#')#! $,#FH7'F3F3F3FV#\"%c8FN7'F3F3F3F3#!&)p8\"%v5F8" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 80 "# approximate LU decomposition\n(P,L,U) := Lin earAlgebra:-LUDecomposition(1.0*A);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6 #>6%%\"PG%\"LG%\"UG6%-%'RTABLEG6%\"*k$)QY\"-%'MATRIXG6#7'7'\"\"!F2F2F2 \"\"\"7'F2F2F2F3F27'F3F2F2F2F27'F2F2F3F2F27'F2F3F2F2F2%'MatrixG-F*6%\" *?5)z9-F.6#7'7'$\"#5!\"\"$F2F2FCFCFC7'$!3ywxxxxxxx!#=F@FCFCFC7'FE$\"3% *4$z8C$\"3E_X5mc[%Q%FGF@F C7'$\"3ywxxxxxxxFG$\"3Q$z8CC " 0 "" {MPLTEXT 1 0 30 "LinearAlgebra:-Transpose(P).P;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*CXgY\"-%'MATRIXG6#7'7'\"\"\" \"\"!F-F-F-7'F-F,F-F-F-7'F-F-F,F-F-7'F-F-F-F,F-7'F-F-F-F-F,%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "B := LinearAlgebra:-Matri xInverse(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'RTABLEG6%\"*? NnZ\"-%'MATRIXG6#7'7'#!$J\"\"$h(#!#\")\"%A:#!#BF3#!$9\"F0#\"$x\"F37'#! %:5\"%\\o#!$D\"F=#\"$Z&F=#!#qF=#!$1#F=7'#\"$l$\"%$G##\"$^&\"%mX#!$x)FL #!$6#FI#!$L\"FL7'#!$r&FI#!$%GFI#\"$?#FI#!$L%FI#\"$E#FI7'#\"$f*F=#!%<9 \"&)p8#!$.(F]o#\"%Z7F=#!%v5F]o%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "B.A;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\" *?lbY\"-%'MATRIXG6#7'7'\"\"\"\"\"!F-F-F-7'F-F,F-F-F-7'F-F-F,F-F-7'F-F- F-F,F-7'F-F-F-F-F,%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "C := LinearAlgebra:-MatrixInverse(1.0*A); # approximate inverse o f A" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'RTABLEG6%\"*!=s\"[\"-% 'MATRIXG6#7'7'$!33BDG&=>9s\"!#=$!3AO7Y4[%>K&!#>$!3$Qj(z8&p6^\"F3$!33H) H$4*G!)\\\"F0$\"3[)y+a\\VH;\"F07'$!3![%e`q\"o>[\"F0$!3'e(='Q&R3D=F3$\" 3cv&*4#Qnl)zF3$!3FaE;9q/A5F3$!3LtV'fNQx+$F37'$\"3G0IeVNx)f\"F0$\"3jtMH 5bu17F0$!35SU/`$=2#>F0$!3OWlNU^AU#*F3$!3JfNO!*R$G\"HF37'$!3F " 0 "" {MPLTEXT 1 0 4 "C.A;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*#\\A'[\"-%'MATRIXG6#7'7 '$\"\"\"\"\"!$!3SE\"z$G6Dh:!#M$!3O$*44P.?`\")F1$!3Kcmu%*R')*)RF1$\"3_o @& pWpMF17'$\"3ac^iCIA56F;$\"31u')o%osmK)F1F>F,FO7'F>$F.F.$\"3]o@ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 34 "Singular Value Decomposition (SVD)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 469 "#\n# Singular value d ecomposition in Matlab style\n#\nsvd := proc( A :: Matrix )\n local UU, SS, VV, V0, m, n, k, s;\n\n m,n := LinearAlgebra[Dimension](A); \n\n # apply Maple SingularValues\n UU,s,V0 := LinearAlgebra[Singu larValues](A,\n output=['U','S','Vt']);\n\n # rearr age output\n k := min(m,n);\n SS := LinearAlgebra[DiagonalMatrix]( s[1..k],m,n); # get a mxn zero matrix\n VV := LinearAlgebra[Transpo se](V0);\n\n return UU, SS, VV;\n\nend proc;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "read \"c:/a aa/apatools/matrix/svd.mpl\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "U, S, V := svd(1.0*A);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>6%%\" UG%\"SG%\"VG6%-%'RTABLEG6%\"*#fEt9-%'MATRIXG6#7'7'$!3WKzcnp$y/&!#=$\"3 U]*>_<$)zk$F4$\"3F:AN))e>2;F4$!3(QQ7TXA9`\"F4$!3&QzY$H[@-vF47'$\"3I/;y %*)Qkv#F4$\"3#QQ$z24+'3\"F4$!3q>8Fe([)R\")F4$!3,DG`TU[5XF4$!3'y*3/71m \\@F47'$!3M&y9J#3a39&F4 $\"3+l5QcZC)3$F47'$\"3:r$RDQwXW&F4$\"3ow3u^2DQ7F4$!3I!pSm)=3@f!#>$\"3_ XNEpS,$)oF4$!3sc(RhbIJf%F47'$\"3'G$>uIY(4;$F4$\"3A(4n]7S8[)F4$\"39%yRM 1H8Z#F4$!3uhQRf_Vs=F4$\"3sddGZx))3HF4%'MatrixG-F*6%\"*OO)y9-F.6#7'7'$ \"3IiyZwuwZ?!#;\"\"!F_pF_pF_p7'F_p$\"3KZ2P[oyk9F^pF_pF_pF_p7'F_pF_p$\" 39Ixq%ypt1(!#e5E->FfpFdo-F*6%\"*O<4Z\"-F.6#7'7'$\"3U'pvrUEAB(F4$\"3ALG=vwss\"*FZ $\"3;69h\\J7&H%F4$!39@V21p9&z#F4$\"3.;=/w]!z`%F47'$\"3k%)3P!\\\">fEF4$ !3?zo7rY*32)F4$!3/!H%4_ZE@RF4$\"3M:?dWHb(R#F4$\"3gq28%*Ri\"e#F47'$!3# \\um(Hy-f8F4$!3k8s8,s@(f%F4$\"3wh[.mW^)\\\"F4$!3>ya1jGE5!)F4$!3'GLjNJ7 rD$F47'$!3!\\oq(4hW9iF4$!3K&=Zr.Die\"F4$\"3%zhSp$o<`MF4$!3t]()oR^UU " 0 "" {MPLTEXT 1 0 35 "U.S.LinearAlgebra:-Transpose(V), A;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6$-%'RTABLEG6%\"*_\"[p9-%'MATRIXG6#7'7'$!3A)********** ***p!#<$!37**************zF.$!3gov;()zx!\\\"!#K$\"3y,++++++]F.$!2c**** ***********F.7'$\"3+/++++++?F.$\"3y$*************>F.$!2M&)************ *F.$!3y,++++++gF.$!3a6++++++]F.7'$!3m%**************)F.$!3)3+++++++&F. $!3C')************HF.$\"3c.++++++]F.$!3W/++++++SF.7'$\"3y$************ *pF.$\"3y,++++++?F.$!3W'*************RF.$!3M(*************zF.$\"3+-+++ +++5F.7'$\"3m%*************pF.FD$!\"'\"\"!FF$!\"$Fhn%'MatrixG-F$6%\"*K ik[\"-F(6#7'7'!\"(!\")Fhn\"\"&!\"\"7'\"\"#FhoFfoFgn!\"&7'!\"*FioFjnFeo !\"%7'\"\"(FhoF\\pFdo\"\"\"7'F^pF[pFgnFioFjnF[o" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 76 "# verify that U and V are orthogonal matrices \nU.LinearAlgebra:-Transpose(U);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-% 'RTABLEG6%\"*_m-[\"-%'MATRIXG6#7'7'$\"3m+++++++5!#<$!3Iq/ne(!#M$!3 Q7<'\\<67L$F1$\"3oD#=Cp#F1$!3OX)*o1S#*[BF8$\"3#\\1T-Gf4@#F87'F2F<$\"2))************* **F.$!37xnN2bahCF8$\"31ln*pR.AN\"F87'F4F>FEF:$!3u]^]c#)*3D\"F87'F6F@FG FJFC%'MatrixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 116 "QR decomposition: Every matrix A can be written as \+ A = Q.R, where Q is orthogonal, and R is upper triangular" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "(Q,R) := LinearAlgebra:-QRDecomposition(1.0*A);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>6$%\"QG%\"RG6$-%'RTABLEG6%\"*CXoZ\"-%'MATRIXG6#7' 7'$!3o!H!4]^s&f%!#=$\"3)=P\"RJ\\J?\\F3$\"3.Dbwo%yBs#F3$!3'e(H*o-xd[%F3 $!3b8G1F'[#4_F37'$\"3sDsfGV188F3$!3![)4)3aEI=\"F3$!3K/uy_aa'e#F3$!35R5 $\\vm=o)F3$\"3!yr^;\"Ha[QF37'$!39;voy%*y3fF3$\"3WXFt!GJZ?#F3$!3'fsK8$y *oH(F3$\"3I.'z%QSAE=F3$\"3%=`I(oNL4>F37'$\"3e*G!4]^s&f%F3$!3[z$Qa,F)>C !#>$!3!e&)o5/*[5dF3$!3^dn0#>8Kt&FW$!3K\"ykG!GltnF37'FS$\"3v1L%)>(f\\L) F3$!3s%4qz'GX)4#FW$\"3Wp[_g)*zg\"*FW$\"3G-$pA$zn>HF3%'MatrixG-F)6%\"*) )>;[\"-F-6#7'7'$\"3c\"ys6iaJ_\"!#;$\"3cKA2?,ewO!#<$!33dPMRZRaHF^p$!3ah kmgQX,7F[p$\"3ykt;76TZ7F^p7'$\"\"!Fgp$!3sSB==$3DG\"F[p$!3%\\LX%)HF3$!3z=\"*4@p42LF^p7'FfpFfp$\"3m1V=$oEy&[F^p$\"3(GVUmY \")z$RF^p$\"3kdC)Rp)pJMF^p7'FfpFfpFfp$\"3UM-4@1'*zQF^p$\"3nim-P`'os$F^ p7'FfpFfpFfpFfp$!3()e!z0o[.s$F^pFao" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Q.R, A;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6$-%'RTABLEG6 %\"*?kfZ\"-%'MATRIXG6#7'7'$!3y,++++++q!#<$!3y,++++++!)F.$!39vUGpJqo%)! #L$\"3c.++++++]F.$!35,++++++5F.7'$\"\"#\"\"!$\"3M**************>F.$!27 )**************F.$!3y,++++++gF.$!\"&F;7'$!3y,++++++!*F.$!3)3+++++++&F. $!\"$F;$\"3y,++++++]F.$!\"%F;7'$\"\"(F;$\"3W+++++++?F.FMF/$\"3A+++++++ 5F.7'FP$!\"*F;F@FBFI%'MatrixG-F$6%\"*Kik[\"-F(6#7'7'!\"(!\")F;\"\"&!\" \"7'F:F:F^o!\"'FC7'FXFCFJF]oFN7'FQF:FNF\\o\"\"\"7'FQFXF`oFCFJFY" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "T := Q.LinearAlgebra:-Transp ose(Q);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"TG-%'RTABLEG6%\"*CZ5Z\" -%'MATRIXG6#7'7'$\"3A+++++++5!#<$!3k'4vsd^9;\"!#M$\"3S47XRCj5:!#L$\"39 X8\"o(\\cG_F3$\"3%Q:YKKiv:#F37'F1$\"\"\"\"\"!$!3[.%Q&)GR%zyF3$\"3?,k-d @\"*pXF3$!3t'Q^9YhbT\"F67'F4F?F<$!3.,zq'3\"*)R=F6$\"3&o(GETcCFJ!#N7'F7 FAFFF.$!3u3z(4iRZ0$F37'F9FCFHFLF.%'MatrixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 256 382 "ClearM atrix := proc( A :: Matrix,\n tol :: numeric )\n local B, m, n, j, k;\n\n m, n := LinearAlgebra:-Dimension(A);\n \+ B := Matrix(m, n);\n\n for j from 1 to m do\n for k from 1 to \+ n do\n if abs(A[j,k]) < tol then\n B[j,k] := 0;\n \+ else\n B[j,k] := A[j,k];\n end if;\n en d do;\n end do;\n\n return B;\nend proc;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "read \"c:/304/cle armatrix.txt\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "ClearMat rix(T,10.0^(-12));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*G %fs9-%'MATRIXG6#7'7'$\"3A+++++++5!#<\"\"!F/F/F/7'F/$\"\"\"F/F/F/F/7'F/ F/F1F/F/7'F/F/F/F,F/7'F/F/F/F/F,%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" 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