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{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "A:=matrix(4,4,[4/3,3/4,8/3,-1/12,2,
1,0,-1,4,1/2,-1,5/2,-2/3,-2,-4/3,2/3]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"AGK%'matrixG6#7&7&#\"\"%\"\"$#F,F+#\"\")F,#!\"\"\"#77&\"\"#
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{MPLTEXT 1 0 14 "B:=evalm(A-3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gaussjord(B^2);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#K%'matrixG6#7&7&\"\"\"\"\"!!\"\"#F(\"\"#7&F)F(F
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "B:=evalm(A+2):" }}}{EXCHG 
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{XPPMATH 20 "6#K%'matrixG6#7&7&\"\"\"\"\"!F)F(7&F)F(F)!\"\"7&F)F)F(F+7
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q3:=[-1,1,1,1]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gaussjor
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11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7&7#,**&#\"\"\"\"\"#F+*&%#c1GF+-
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "simplify(evalm([seq(diff(y[i],x),i=
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'F'F'Q*pprint1086\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "rest
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{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q8" }{MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "A:=matrix(3,3,[3,3,-3,1,-1,1,1,3,-3
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{MPLTEXT 1 0 15 "eigenvalues(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"
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{MPLTEXT 1 0 28 "y1:=evalm([3,1,1]*exp(3*x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#y1GK%'vectorG6#7%,$*&\"\"$\"\"\"-%$expG6#,$*&F+F,%\"
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0 13 "gaussjord(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7%7
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" 0 "" {MPLTEXT 1 0 19 "y2:=evalm([0,1,1]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#y2GK%'vectorG6#7%\"\"!\"\"\"F*Q*pprint1136\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gaussjord(A+4);" }}{PARA 11 
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1 0 30 "y3:=evalm([6,-5,9]*exp(-4*x));" }}{PARA 11 "" 1 "" {XPPMATH 
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "Y:=augment(y1,y2,y3);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"YGK%'matrixG6#7%7%,$*&\"\"$\"\"\"-%$expG6#,$
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "aux:=linsolve(Y,[1,0,0]);" }}{PARA 
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "aux:=[seq(int(aux[i],x),i=1.
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "yp:=evalm(Y&*aux);" }}{PARA 
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 " 0 "" {MPLTEXT 1 0 14 "matrix(3,1,%);" }}{PARA 11 "" 1 "" {XPPMATH 
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{XPPMATH 20 "6#K%'matrixG6#7%7%\"\"\"\"\"!F)7%F)F(F)7%F)F)F)Q*pprint12
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "y1:=evalm(q1*exp(2*x)):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "gaussjord(A+1-I);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7%7%\"\"\"\"\"!^$#\"\"(\"\"&#F(F
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0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "y2:=[seq(Im(yc[i]),i
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i]),i=1..3)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "y:=evalm(c
1*y1+c2*y2+c3*y3+yp):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "ma
trix(3,1,%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7%7#,(*&%#
c2G\"\"\",&*(\"\"(F+-%$expG6#,$%#x|irG!\"\"F+-%$sinG6#F3F+F+*&F/F+-%$c
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "simplify(evalm([seq(diff(y[i],x),i=
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\"\"!F(Q*pprint1266\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "re
start:with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the prote
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "A:=matrix(4,8,[1,2,1/2,1,1,0
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}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGK%'matrixG6#7&7*\"\"\"\"\"##F*F
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!\"##!\"\"F+!\"'F-F-F-F*Q*pprint1276\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "A:=addrow(A,1,2,12);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%\"AGK%'matrixG6#7&7*\"\"\"\"\"##F*F+F*F*\"\"!F-F-7*F-\"#L\"\")\"#
G\"#7F*F-F-7*F0!\")!\"$!#7F-F-F*F-7*\"\"'!\"##!\"\"F+!\"'F-F-F-F*Q*ppr
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3,-8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGK%'matrixG6#7&7*\"\"\"
\"\"##F*F+F*F*\"\"!F-F-7*F-\"#L\"\")\"#G\"#7F*F-F-7*F-!#C!\"(!#?!\")F-
F*F-7*\"\"'!\"##!\"\"F+!\"'F-F-F-F*Q*pprint1296\"" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 20 "A:=addrow(A,1,4,-6);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"AGK%'matrixG6#7&7*\"\"\"\"\"##F*F+F*F*\"\"!F-F-7*F-
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F*Q*pprint1306\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "A:=mulr
ow(A,2,1/33);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGK%'matrixG6#7&7
*\"\"\"\"\"##F*F+F*F*\"\"!F-F-7*F-F*#\"\")\"#L#\"#GF1#\"\"%\"#6#F*F1F-
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "A:=addrow(A,2,1,-2);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGK%'matrixG6#7&7*\"\"\"\"\"!#F*\"
#m#!#B\"#L#\"\"$\"#6#!\"#F0F+F+7*F+F*#\"\")F0#\"#GF0#\"\"%F3#F*F0F+F+7
*F+!#C!\"(!#?!\")F+F*F+7*F+!#9#F@\"\"#!#7!\"'F+F+F*Q*pprint1326\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "A:=addrow(A,2,3,24);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGK%'matrixG6#7&7*\"\"\"\"\"!#F*\"
#m#!#B\"#L#\"\"$\"#6#!\"#F0F+F+7*F+F*#\"\")F0#\"#GF0#\"\"%F3#F*F0F+F+7
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGK%'matrixG6#7&7*\"\"\"\"\"!#F*\"
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\"!#F*\"#m#!#B\"#L#\"\"$\"#6#!\"#F0F+F+7*F+F*#\"\")F0#\"#GF0#\"\"%F3#F
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addrow(A,3,1,-1/66);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGK%'matri
xG6#7&7*\"\"\"\"\"!F+#!\"*\"#8#\"#6\"#R#!\"#F1#F*\"#yF+7*F+F*#\"\")\"#
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{MPLTEXT 1 0 23 "A:=addrow(A,3,2,-8/33);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"AGK%'matrixG6#7&7*\"\"\"\"\"!F+#!\"*\"#8#\"#6\"#R#!\"#F1#F*
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "A:=addrow(A,3,4,7/66);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGK%'matrixG6#7&7*\"\"\"\"\"!F+#!
\"*\"#8#\"#6\"#R#!\"#F1#F*\"#yF+7*F+F*F+#\"#7F.#\"#?F1#\"\"(F1#\"\")F1
F+7*F+F+F*#!\"%F.#!\")F.FB#!#6F.F+7*F+F+F+#F3F.#!#QF1#\"#9F1#!\"(F5F*Q
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\"\"\"\"\"!F+#!\"*\"#8#\"#6\"#R#!\"#F1#F*\"#yF+7*F+F*F+#\"#7F.#\"#?F1#
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!\"(FI#F<F8#!#8\"\"#Q*pprint1396\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "A:=addrow(A,4,1,9/13);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"AGK%'matrixG6#7&7*\"\"\"\"\"!F+F+#\"#9\"\"$#!\"&F.#\"\"&\"#7
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "A:=addrow(A,4,2,-12/13);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGK%'matrixG6#7&7*\"\"\"\"\"!F+F+#
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\"'7*F+F+F*#!\"%\"#8#!\")FBFC#!#6FBF+7*F+F+F+F*#\"#>F.#!\"(F.#F;F3#!#8
F6Q*pprint1416\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "A:=addr
ow(A,4,3,4/13);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGK%'matrixG6#7
&7*\"\"\"\"\"!F+F+#\"#9\"\"$#!\"&F.#\"\"&\"#7#!\"*\"\"#7*F+F*F+F+#!#;F
.#\"\"(F.#!\"\"F.\"\"'7*F+F+F*F+#\"\"%F.#!\"%F.#!\"#F.FE7*F+F+F+F*#\"#
>F.#!\"(F.#F;F3#!#8F6Q*pprint1426\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 47 "Determinant (the product of 'mulrow' divisors):" }{MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "33*(-13/11)*(-2/13);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"'" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 3 "Q11" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 63 "A:=matrix(4,4,[1,2,1/2,1,-12,9,2,16,8,-8,-3,-12,6,-2,
-1/2,-6]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGK%'matrixG6#7&7&\"
\"\"\"\"##F*F+F*7&!#7\"\"*F+\"#;7&\"\")!\")!\"$F.7&\"\"'!\"##!\"\"F+!
\"'Q*pprint1436\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "trace(A
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 88 "for i to 4 do for j from i+1 to 4 do print(det(s
ubmatrix(A,[i,j],[i,j]))) end do end do;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"#L" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"(" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!#6" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#!#A" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#7
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 136 "det(submatrix(A,[1,2,3
],[1,2,3]))+det(submatrix(A,[1,2,4],[1,2,4]))+det(submatrix(A,[1,3,4],
[1,3,4]))+det(submatrix(A,[2,3,4],[2,3,4]));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "det(
A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"'" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 25 "Characteristic polynomial" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "p:=L^4-L^3-7*L^2+L+6;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG,,*$)%\"LG\"\"%\"\"\"F**$)F(\"\"
$F*!\"\"*&\"\"(F*)F(\"\"#F*F.F(F*\"\"'F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "p:=simplify(p/(L-1));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"pG,(*$)%\"LG\"\"$\"\"\"F**&\"\"(F*F(F*!\"\"\"\"'F-" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "p:=simplify(p/(L+1));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG,(*$)%\"LG\"\"#\"\"\"F*F(!\"\"\"
\"'F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "The roots are:  1,  -1, \+
 -2 and 3" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 15 "gaussjord(A-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7
&7&\"\"\"\"\"!F)!\"\"7&F)F(F)#F(\"\"#7&F)F)F(F)7&F)F)F)F)Q*pprint1446
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "q1:=[1,-1/2,0,1];" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#q1G7&\"\"\"#!\"\"\"\"#\"\"!F&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gaussjord(A+1);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#K%'matrixG6#7&7&\"\"\"\"\"!F)#!\"\"\"\"#7&F)F(F
)F(7&F)F)F(F)7&F)F)F)F)Q*pprint1456\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "q2:=[1/2,-1,0,1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%#q2G7&#\"\"\"\"\"#!\"\"\"\"!F'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "gaussjord(A+2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%
'matrixG6#7&7&\"\"\"\"\"!F)#!\"\"\"\"$7&F)F(F)#\"\"%F,7&F)F)F(#!\"%F,7
&F)F)F)F)Q*pprint1466\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "
q3:=[1,-4,4,3];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#q3G7&\"\"\"!\"%
\"\"%\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gaussjord(A-3
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7&7&\"\"\"\"\"!F)!\"
#7&F)F(F)F*7&F)F)F(\"\"#7&F)F)F)F)Q*pprint1476\"" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 15 "q4:=[2,2,-2,1];" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#q4G7&\"\"#F&!\"#\"\"\"" }}}}{MARK "87" 0 }{VIEWOPTS 1 1 0 1 
1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }