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{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" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 58 "A:=matrix(4,4,[1,-1,-2,0,1,2,1,-1,-1,-3,-2,1,-4,-2,-6
,4]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7&\"\"\"!
\"\"!\"#\"\"!7&F*\"\"#F*F+7&F+!\"$F,F*7&!\"%F,!\"'\"\"%" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eigenvalues(A);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6&!\"\"\"\"#F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 39 "B:=evalm(A+Matrix(4,4,shape=identity));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"BG-%'matrixG6#7&7&\"\"#!\"\"!\"#\"\"!7&\"\"\"\"\"$F
/F+7&F+!\"$F+F/7&!\"%F,!\"'\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "linsolve(B,[0,0,0,0]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#-%'vectorG6#7&&%#_tG6#\"\"\"\"\"!F',$F'\"\"#" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 13 "q:=[1,0,1,2];" }}{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#-%'ve
ctorG6#7&!\"\"\"\"!F'!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
21 "y1:=evalm(q*exp(-x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G-%'
vectorG6#7&-%$expG6#,$%\"xG!\"\"\"\"!F),$F)\"\"#" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 41 "evalm([seq(diff(y1[i],x),i=1..4)]-A&*y1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&\"\"!F'F'F'" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "B:=evalm(A-2*Matrix(4,4,shape=ident
ity)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "linsolve(B,[0,0,0
,0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&,$&%#_tG6#\"\"
\"!\"\"F'F(\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "q:=[1,1
,-1,0]:" }}}{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 22 "y2:=evalm(q*exp(2*x));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y2G-%'vectorG6#7&-%$expG6#,$%\"xG\"
\"#F),$F)!\"\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "eval
m([seq(diff(y2[i],x),i=1..4)]-A&*y2);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#-%'vectorG6#7&\"\"!F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 15 "B2:=evalm(B^2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "li
nsolve(B2,[0,0,0,0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7
&&%#_tG6#\"\"\",$&F(6#\"\"#!\"\"F,,&F'F.*&F.F*F,F*F*" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 13 "s:=[1,0,0,2]:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 15 "q:=evalm(B&*s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%\"qG-%'vectorG6#7&!\"\"F)\"\"\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "y3:=evalm((q*x+s)*exp(2*x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#y3G-%'vectorG6#7&*&-%$expG6#,$%\"xG\"\"#\"\"\",&F.!
\"\"F0F0F0,$*&F*F0F.F0F2F4,$F*F/" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 "simplify(evalm([seq(diff(y3[i],x),i=1..4)]-A&*y3));" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&\"\"!F'F'F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "B3:=evalm(B^3):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "linsolve(B3,[0,0,0,0]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&&%#_tG6#\"\"\",$&F(6#\"\"#!\"
\"F,&F(6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "u:=[1,0,0
,0]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "s:=evalm(B&*u);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG-%'vectorG6#7&!\"\"\"\"\"F)!\"%
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "q:=evalm(B&*s);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG-%'vectorG6#7&\"\"#F)!\"#\"\"!" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "y4:=evalm((q*x^2/2+s*x+u)
*exp(2*x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y4G-%'vectorG6#7&*&-
%$expG6#,$%\"xG\"\"#\"\"\",(*$)F.F/F0F0F.!\"\"F0F0F0*&F*F0,&F2F0F.F0F0
*&F*F0,&F2F4F.F4F0,$*&F*F0F.F0!\"%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 "simplify(evalm([seq(diff(y4[i],x),i=1..4)]-A&*y4));" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&\"\"!F'F'F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Y:=augment(y1,y2,y3,y4);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"YG-%'matrixG6#7&7&-%$expG6#,$%\"xG
!\"\"-F+6#,$F.\"\"#*&F0\"\"\",&F.F/F5F5F5*&F0F5,(*$)F.F3F5F5F.F/F5F5F5
7&\"\"!F0,$*&F0F5F.F5F/*&F0F5,&F9F5F.F5F57&F*,$F0F/F>*&F0F5,&F9F/F.F/F
57&,$F*F3F<,$F0F3,$F>!\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
16 "yp:=[0,1/x,0,0];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ypG7&\"\"!*
&\"\"\"F(%\"xG!\"\"F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "
simplify(evalm([seq(diff(yp[i],x),i=1..4)]-A&*yp));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%'vectorG6#7&*&\"\"\"F(%\"xG!\"\",$*&,&F)\"\"#F(F(F(
F)!\"#F*,$F'\"\"$,$F'F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "
r:=evalm([1,-2-1/x,3,2]/x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG-
%'vectorG6#7&*&\"\"\"F*%\"xG!\"\"*&F+F,,&!\"#F*F)F,F*,$F)\"\"$,$F)\"\"
#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "aux:=simplify(evalm(in
verse(Y)&*r));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$auxG-%'vectorG6#7
&*(-%$expG6#%\"xG\"\"\",&F-F.F.!\"\"F.F-!\"#*(-F+6#,$F-F1F.,**$)F-\"\"
$F.\"\"#*$)F-F:F.F0*&F:F.F-F.F0F.F0F.F-F1*(F3F.,(F;\"\"%*&F:F.F-F.F.F.
F.F.F-F1*(F3F.F-F1,&F-F:F.F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 43 "aux:=[seq(simplify(int(aux[i],x)),i=1..4)];" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%$auxG7&*&-%$expG6#%\"xG\"\"\"F*!\"\",$*(-F(6#,$F*!
\"#F+,&*$)F*\"\"#F+F+F+F,F+F*F,F,,$*(F/F+,&F*F6F+F+F+F*F,F,,$*&F/F+F*F
,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "yp:=simplify(evalm(Y
&*aux));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ypG-%'vectorG6#7&\"\"!*
&\"\"\"F+%\"xG!\"\"F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "
simplify(evalm([seq(diff(yp[i],x),i=1..4)]-A&*yp-r));" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#-%'vectorG6#7&\"\"!F'F'F'" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 30 "y:=evalm(yp+Y&*[c1,c2,c3,c4]):" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 51 "simplify(evalm([seq(diff(y[i],x),i=1..4)]
-A&*y-r));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&\"\"!F'F'F
'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 0 }
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