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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "x:=[1,2,3,4,5];  y:=
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "for i to 3 do for j to 3 do A[i,j]:
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{XPPMATH 20 "6#>%\"BG7%$\"+nmmm[!\"*$\"#5\"\"!$\"$L$F+" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 ">
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{XPPMATH 20 "6#>%\"CG-%'matrixG6#7%7&$\"+66hj9!\"*$\"+LLL$G#F,$\"+++++
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7&7&$\"&:0#\"\"!$\"$
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{MPLTEXT 1 0 32 "C:=addrow(C,1,2,-C[2,1]/C[1,1]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"CG-%'matrixG6#7&7&$\"&:0#\"\"!$\"$D#F,$\"+++++b!\")
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> " 0 "" {MPLTEXT 1 0 32 "C:=addrow(C,1,3,-C[3,1]/C[1,1]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7&7&$\"&:0#\"\"!$\"$D#F,$
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "C:=addrow(C,2,3,-C[3,2]/C[2,2]);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7&7&$\"&:0#\"\"!$\"
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG$!+a*>+=\"!\"*" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 28 "b:=(C[2,4]-a*C[2,3])/C[2,2];" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%\"bG$\"+#G_'*G$!\"*" }}}{EXCHG {PARA 0 "> " 
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{XPPMATH 20 "6#>%\"cG$!+IARo;!#6" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "evalm(A &* [a,b,c]);" }}{PARA 11 "" 1 "" {XPPMATH 20 
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "restart:  with(linalg):" }}
{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra
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{MPLTEXT 1 0 15 "A:=matrix(4,4):" }}}{EXCHG {PARA 0 "> " 0 "" 
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nd do end do;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalm(A);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&$\"+F9j^7!#5$!+_rG**
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{MPLTEXT 1 0 27 "B:=[seq(tan(i*2.),i=1..4)];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"BG7&$!+j)R]=#!\"*$\"+#G@y:\"F($!+9>15H!#5$!+b9r*z'F
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7&7'$\"+F9j^7!#5$!+_
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ckmatrix(C,[a,b,c,d,_]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'m
atrixG6#7'7'$\"+F9j^7!#5$!+_rG**o!#6$!+$G\\:5$F,$!+&f'3'G'F,$!+j)R]=#!
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\"+\\m'y(eF,$\"+#HO+q%F,$\"+mBskLF,$\"+ob@B=F,$!+9>15HF,7'$\"+:q&od(F,
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_G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "C:=swaprow(C,4,1);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7'7'$\"+:q&od(!#5$
\"+(GcCf'F,$\"+nLY+bF,$\"+Y,WuUF,$!+b9r*z'!\"*7'$\"+DD#*HQF,$\"+$y()QO
#F,$\"+X@&QX'!#6$!+P%35V\"F,$\"+#G@y:\"F57'$\"+\\m'y(eF,$\"+#HO+q%F,$
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&f'3'G'F,$!+j)R]=#F57'%\"aG%\"bG%\"cG%\"dG%\"_G" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 60 "for i from 2 to 4 do C:=addrow(C,1,i,-C[i,1]/C
[1,1]) end do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7'
7'$\"+:q&od(!#5$\"+(GcCf'F,$\"+nLY+bF,$\"+Y,WuUF,$!+b9r*z'!\"*7'$\"\"!
F8$!*!RV%o*F,$!+#Hp\\8#F,$!+?rj\"f$F,$\"+b]\"\\f%F57'$\"+\\m'y(eF,$\"+
#HO+q%F,$\"+mBskLF,$\"+ob@B=F,$!+9>15HF,7'$\"+F9j^7F,$!+_rG**o!#6$!+$G
\\:5$F,$!+&f'3'G'F,$!+j)R]=#F57'%\"aG%\"bG%\"cG%\"dG%\"_G" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7'7'$\"+:q&od(!#5$\"+(GcCf'F,
$\"+nLY+bF,$\"+Y,WuUF,$!+b9r*z'!\"*7'$\"\"!F8$!*!RV%o*F,$!+#Hp\\8#F,$!
+?rj\"f$F,$\"+b]\"\\f%F57'F7$!*Df;9%F,$!*v!\\B!*F,$!+r*[F\\\"F,$\"++v(
R)\\F57'$\"+F9j^7F,$!+_rG**o!#6$!+$G\\:5$F,$!+&f'3'G'F,$!+j)R]=#F57'%
\"aG%\"bG%\"cG%\"dG%\"_G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'m
atrixG6#7'7'$\"+:q&od(!#5$\"+(GcCf'F,$\"+nLY+bF,$\"+Y,WuUF,$!+b9r*z'!
\"*7'$\"\"!F8$!*!RV%o*F,$!+#Hp\\8#F,$!+?rj\"f$F,$\"+b]\"\\f%F57'F7$!*D
f;9%F,$!*v!\\B!*F,$!+r*[F\\\"F,$\"++v(R)\\F57'F7$!+Kc%*y<F,$!+*Qy,,%F,
$!+Rs=#*pF,$!+!='yh5F57'%\"aG%\"bG%\"cG%\"dG%\"_G" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 37 "C:=swaprow(C,2,4): C:=swapcol(C,2,4);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7'7'$\"+:q&od(!#5$\"
+Y,WuUF,$\"+nLY+bF,$\"+(GcCf'F,$!+b9r*z'!\"*7'$\"\"!F8$!+Rs=#*pF,$!+*Q
y,,%F,$!+Kc%*y<F,$!+!='yh5F57'F7$!+r*[F\\\"F,$!*v!\\B!*F,$!*Df;9%F,$\"
++v(R)\\F57'F7$!+?rj\"f$F,$!+#Hp\\8#F,$!*!RV%o*F,$\"+b]\"\\f%F57'%\"aG
%\"dG%\"cG%\"bG%\"_G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "for
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"" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7'7'$\"+:q&od(!#5$\"+Y,WuUF,$
\"+nLY+bF,$\"+(GcCf'F,$!+b9r*z'!\"*7'$\"\"!F8$!+Rs=#*pF,$!+*Qy,,%F,$!+
Kc%*y<F,$!+!='yh5F57'F7F7$!*QfBi%!#6$!*/:#QMFD$\"+Xil5_F57'F7$!+?rj\"f
$F,$!+#Hp\\8#F,$!*!RV%o*F,$\"+b]\"\\f%F57'%\"aG%\"dG%\"cG%\"bG%\"_G" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7'7'$\"+:q&od(!#5$
\"+Y,WuUF,$\"+nLY+bF,$\"+(GcCf'F,$!+b9r*z'!\"*7'$\"\"!F8$!+Rs=#*pF,$!+
*Qy,,%F,$!+Kc%*y<F,$!+!='yh5F57'F7F7$!*QfBi%!#6$!*/:#QMFD$\"+Xil5_F57'
F7F7$!)FP3vF,$!*u[iY&FD$\"+MnJS^F57'%\"aG%\"dG%\"cG%\"bG%\"_G" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "C:=swaprow(C,3,4);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7'7'$\"+:q&od(!#5$\"+Y,WuU
F,$\"+nLY+bF,$\"+(GcCf'F,$!+b9r*z'!\"*7'$\"\"!F8$!+Rs=#*pF,$!+*Qy,,%F,
$!+Kc%*y<F,$!+!='yh5F57'F7F7$!)FP3vF,$!*u[iY&!#6$\"+MnJS^F57'F7F7$!*Qf
Bi%FF$!*/:#QMFF$\"+Xil5_F57'%\"aG%\"dG%\"cG%\"bG%\"_G" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "C:=addrow(C,3,4,-C[4,3]/C[3,3]);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7'7'$\"+:q&od(!#5$
\"+Y,WuUF,$\"+nLY+bF,$\"+(GcCf'F,$!+b9r*z'!\"*7'$\"\"!F8$!+Rs=#*pF,$!+
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7F7F7$!)lH/t!#7$\"+=o8Y?F57'%\"aG%\"dG%\"cG%\"bG%\"_G" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "b:=C[4,5]/C[4,4];" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%\"bG$!+B%y7!G!\"&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "c:=(C[3,5]-b*C[3,4])/C[3,3];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"cG$\"++o#4(>!\"&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "d:=(C[2,5]-b*C[2,4]-c*C[2,3])/C[2,2];" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"dG$!+G*3_<%!\"'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 46 "a:=(C[1,5]-b*C[1,4]-c*C[1,3]-d*C[1,2])/C[1,1];" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG$\"+B%p6C\"!\"&" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "evalm(A &* [a,b,c,d]);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&$!(P]=#!\"'$\")_#y:\"!\"($!(()*4H
F,$!(2(*z'F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalm(B);" }
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