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{MPLTEXT 1 0 27 "y:=evalm(q*exp((2+3*I)*x));" }}{PARA 11 "" 1 "" 
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{MPLTEXT 1 0 15 "assume(x,real);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "y1:=[seq(Re(y[i]),i=1..2)];" }}{PARA 11 "" 1 "" 
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" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7&\"\"\"!\"\"!\"#\"\"!7&F*\"\"#F*
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{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "-1, 2, 2, 2" }{MPLTEXT 1 0 0 "" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gaussjord(A+1);" }}{PARA 
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{MPLTEXT 1 0 34 "gaussjord(stackmatrix((A-2)^2,q));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%'matrixG6#7'7&\"\"\"\"\"!F)#!\"\"\"\"$7&F)F(F)#F(\"
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" {XPPMATH 20 "6#>%\"YG-%'matrixG6#7&7&-%$expG6#,$%\"xG!\"\",$-F+6#,$*
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{MPLTEXT 1 0 27 "y:=evalm(Y&*[C1,C2,C3,C4]):" }}}{EXCHG {PARA 0 "> " 
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "gaussjord(augment(Y,r));" }}{PARA 
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"c:=[seq(simplify(int(cp[i],x)),i=1..4)];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"cG7&*&%\"xG!\"\"-%$expG6#F'\"\"\",$*&#F,\"\"$F,*(-F
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" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "a[0]:=[1,-3,2,4]:  a[1]
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{MPLTEXT 1 0 42 "r:=evalm((a[0]+a[1]*x+a[2]*x^2)*exp(3*x));" }}{PARA 
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG6#7&7&!\"#!\"\"F*\"\"!
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{XPPMATH 20 "6#>&%\"bG6#\"\"#-%'vectorG6#7&#\"#H\"\"%\"#5#!#VF.#!#JF'
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{XPPMATH 20 "6#>&%\"bG6#\"\"\"-%'vectorG6#7&#!$t$\"\")!#t#\"$&fF.#\"$B
$\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"bG6#\"\"!-%'vectorG6#7&
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{MPLTEXT 1 0 43 "yp:=evalm((b[0]+b[1]*x+b[2]*x^2)*exp(3*x));" }}{PARA 
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{MPLTEXT 1 0 53 "simplify(evalm([seq(diff(yp[i],x),i=1..4)]-A&*yp-r));
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "P:=[3,-4,2,1]; Q:=[-4,2,5,-3
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"QG7&!\"%\"\"#\"\"&!\"$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "b:=-linsolve(evalm(A^2+1),evalm(A&*
Q-P));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG,$-%'vectorG6#7&#!$=$
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{MPLTEXT 1 0 41 "a:=-linsolve(evalm(A^2+1),evalm(A&*P+Q));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"aG,$-%'vectorG6#7&#\"%,5\"$Z%#\"#$)F,#\"
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "evalm([seq(diff(y[i],x),i=1.
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}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart: with(linalg):" }}
{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra
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{MPLTEXT 1 0 96 "A := matrix([[-25, 43/2, -11, -11/2], [-20, 17, -10, \+
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{XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7&!#D#\"#V\"\"#!#6#F.F-7&!#?\"#<!#5
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"" {MPLTEXT 1 0 15 "gausselim(A-L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#-%'matrixG6#7&7&\"\"(#!#8\"\"#,&\"\"$\"\"\"%\"LG!\"\"#F.F+7&\"\"!,&#
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F.F.,&F+F.F/F07&F3F3F3,$*(F+F0,*\"#=F0*&F-F.F/F.F0*&F@F.)F/F+F.F.*$)F/
F-F.F.F.,&F6F.*&F(F.F/F.F.F0F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 20 "p:=L^3+4*L^2-3*L-18:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 17 "gcd(p,diff(p,L));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"$\"\"
\"%\"LGF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "quo(p,(L+3)^2,
L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"#!\"\"%\"LG\"\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gaussjord(A-2);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"\"\"\"!\"\"#F(7&F)F(F*F(7&F
)F)F)F)F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "y1:=evalm([-2,
-2,1,0]*exp(2*x)):  y2:=evalm([-1,-1,0,1]*exp(2*x)):" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 15 "gaussjord(A+3);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'matrixG6#7&7&\"\"\"\"\"!F)#F(\"\"#7&F)F(F)F)7&F)F)F(
#!\"\"F+7&F)F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "y3:=e
valm([-1,0,1,2]*exp(-3*x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
43 "gaussjord(stackmatrix((A+3)^2,[-1,0,1,2]));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'matrixG6#7'7&\"\"\"\"\"!F)#!\"&\"\"#7&F)F(F)!\"$7&F)
F)F(#!\"\"F,7&F)F)F)F)F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 
"s:=[5,6,1,2]:  qs:=evalm((A+3)&*s):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "y4:=evalm((qs*x+s)*exp(-3*x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#y4G-%'vectorG6#7&*&-%$expG6#,$*&\"\"$\"\"\"%\"xGF0!
\"\"F0,&*&F/F0F1F0F2\"\"&F0F0,$*&\"\"'F0F*F0F0*&F*F0,&*&F/F0F1F0F0F0F0
F0*&F*F0,&*&F8F0F1F0F0\"\"#F0F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 34 "y:=evalm(C1*y1+C2*y2+C3*y3+C4*y4):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 49 "simplify(evalm([seq(diff(y[i],x),i=1..4)]-A&*y));" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&\"\"!F'F'F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(
linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 118 "A:=matrix([[-5
, -2, -4, 1/2, 2], [-22, -2, -10, 1, 10], [14, 4, 12, -3, -6], [6, 4, \+
8, -3, -4], [-8, -2, -2, -1, 4]]):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "gausselim(A-L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%
'matrixG6#7'7'\"\"'\"\"%\"\"),&\"\"$!\"\"%\"LGF-!\"%7'\"\"!#!#;F,,&#\"
#?F,F-F.F-,&F)\"\"\"*(\"\"(F8F,F-F.F8F8#\"#5F,7'F1F1,&#\"\"*\"\"#F8*(
\"\"&F8F*F-F.F8F-,&#FCFAF-*&F*F-F.F8F8,&#F,F)F8F.F-7'F1F1F1,$*(FAF-,(
\"#KF8*&F(F8)F.FAF8F-*$)F.F,F8F8F8,&\"#OF-*&FCF8F.F8F8F-F8*&,(\"#CF8*&
F)F8FOF8F-FPF8F8FRF-7'F1F1F1F1,$*(FAF-,,*$)F.F)F8F8*&F*F8FQF8F-*&FWF8F
OF8F8*&FMF8F.F8F-\"#;F8F8,(*$FOF8F8*&F*F8F.F8F-F\\oF8F-F8" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "quo(L^3-6*L^2+32,L^2-8*L+16,L);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"LG\"\"\"\"\"#F%" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 28 "p:=L^4-8*L^3+24*L^2-32*L+16;" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%\"pG,,*$)%\"LG\"\"%\"\"\"F**&\"\")F*)F(\"\"$F
*!\"\"*&\"#CF*)F(\"\"#F*F**&\"#KF*F(F*F/\"#;F*" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 17 "gcd(p,diff(p,L));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,**$)%\"LG\"\"$\"\"\"F(*&\"\"'F()F&\"\"#F(!\"\"*&\"#7F(
F&F(F(\"\")F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "gcd(%,diff
(%,L));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"LG\"\"#\"\"\"F(*&\"
\"%F(F&F(!\"\"F*F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "gcd(%
,diff(%,L));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"LG\"\"\"\"\"#!\"
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gaussjord(A+2);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7'7'\"\"\"\"\"!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)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "q:=[1,1,0,2,2]:" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 23 "y1:=evalm(q*exp(-2*x));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#y1G-%'vectorG6#7'-%$expG6#,$*&\"\"#\"\"\"%\"xGF/!
\"\"F)\"\"!,$*&F.F/F)F/F/F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
41 "evalm([seq(diff(y1[i],x),i=1..5)]-A&*y1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'vectorG6#7'\"\"!F'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 15 "gaussjord(A-2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
-%'matrixG6#7'7'\"\"\"\"\"!F)F)!\"\"7'F)F(F)F)F(7'F)F)F(F)F(7'F)F)F)F(
\"\"#7'F)F)F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "q:=[1,
-1,-1,-2,1]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "y2:=evalm(q
*exp(2*x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "evalm([seq(d
iff(y2[i],x),i=1..5)]-A&*y2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'ve
ctorG6#7'\"\"!F'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "g
aussjord(stackmatrix((A-2)^2,q));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-
%'matrixG6#7(7'\"\"\"\"\"!F)F)#!\"\"\"\"*7'F)F(F)F)#!\"&\"\"$7'F)F)F(F
)#F(F,7'F)F)F)F(#\"\"#F,7'F)F)F)F)F)F6" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "s:=[1,15,-1,-2,9]:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "qs:=evalm((A-2)&*s):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "y3:=evalm((qs*x+s)*exp(2*x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#y3G-%'vectorG6#7'*&-%$expG6#,$*&\"\"#\"\"\"%\"xGF0F0
F0,&*&\"#;F0F1F0!\"\"F0F0F0*&F*F0,&*&F4F0F1F0F0\"#:F0F0*&F*F0,&*&F4F0F
1F0F0F0F5F0*&F*F0,&*&\"#KF0F1F0F0F/F5F0*&F*F0,&*&F4F0F1F0F5\"\"*F0F0" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "simplify(evalm([seq(diff(
y3[i],x),i=1..5)]-A&*y3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vecto
rG6#7'\"\"!F'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "gaus
sjord(stackmatrix((A-2)^3,q,s));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%
'matrixG6#7)7'\"\"\"\"\"!F)F)#\"\"#\"#@7'F)F(F)F)#F(F+7'F)F)F(F)#!#V\"
#U7'F)F)F)F(#!\"%F,7'F)F)F)F)F)F6F6" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 63 "u:=[-4,-21,43,8,42]: su:=evalm((A-2)&*u): qu:=evalm((
A-2)&*su):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "y4:=evalm((qu
*x^2/2+su*x+u)*exp(2*x));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#y4G-%'
vectorG6#7'*&-%$expG6#,$*&\"\"#\"\"\"%\"xGF0F0F0,(*&\"#yF0)F1F/F0!\"\"
*&\"#9F0F1F0F6\"\"%F6F0*&F*F0,(*&F4F0F5F0F0*&\"$q\"F0F1F0F0\"#@F6F0*&F
*F0,(*&F4F0F5F0F0*&F8F0F1F0F0\"#VF0F0*&F*F0,(*&\"$c\"F0F5F0F0*&\"#GF0F
1F0F0\"\")F0F0*&F*F0,(*&F4F0F5F0F6*&\"#kF0F1F0F0\"#UF0F0" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "simplify(evalm([seq(diff(y4[i],x),i
=1..5)]-A&*y4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7'\"\"
!F'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "gaussjord(stac
kmatrix((A-2)^4,q,s,u));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG
6#7*7'\"\"\"\"\"!F)F)#\"\"$\"\"&7'F)F(F)F)#F(\"\"#7'F)F)F(F)#F+F/7'F)F
)F)F(#!\"'F,7'F)F)F)F)F)F5F5F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 86 "v:=[-6,-5,-15,12,10]: uv:=evalm((A-2)&*v): sv:=evalm((A-2)&*uv
): qv:=evalm((A-2)&*sv):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 
"y5:=evalm((qv*x^3/6+sv*x^2/2+uv*x+v)*exp(2*x));" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%#y5G-%'vectorG6#7'*&-%$expG6#,$*&\"\"#\"\"\"%\"xGF0F0
F0,**&#\"$C%\"\"$F0*$)F1F6F0F0F0*&\"$q\"F0)F1F/F0!\"\"*&\"$Q\"F0F1F0F0
\"\"'F<F0*&F*F0,**&#F5F6F0F7F0F<*&\"$a#F0F;F0F<*&\"$9%F0F1F0F0\"\"&F<F
0*&F*F0,**&#F5F6F0F7F0F<*&F:F0F;F0F0*&\"$]$F0F1F0F<\"#:F<F0*&F*F0,**&#
\"$[)F6F0F7F0F<*&\"$S$F0F;F0F0*&\"$w#F0F1F0F<\"#7F0F0*&F*F0,**&F4F0F7F
0F0*&\"$#QF0F;F0F<*&\"#'*F0F1F0F0\"#5F0F0" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 51 "simplify(evalm([seq(diff(y5[i],x),i=1..5)]-A&*y5));
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7'\"\"!F'F'F'F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "y:=evalm(C1*y1+C2*y2+C3*y3+C
4*y4+C5*y5):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "simplify(ev
alm([seq(diff(y[i],x),i=1..5)]-A&*y));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#-%'vectorG6#7'\"\"!F'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "106 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 
1 1 }{PAGENUMBERS 0 1 2 33 1 1 }