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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "k:=matrix([[3/2,1/2,-1,0],[1
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{XPPMATH 20 "6#>%\"kGK%'matrixG6#7&7&#\"\"$\"\"##\"\"\"F,!\"\"\"\"!7&F
-F-F0F07&F/F0F*#F/F,7&F0F0F3F-Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 15 "eigenvalues(k);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&
\"\"!\"\"\",&#\"\"$\"\"#F$*&F(!\"\"\"\"&#F$F(F$,&F&F$*&F(F*F+F,F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "nullspace(k);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#<#K%'vectorG6#7&\"\"\"!\"\"F(F(Q(pprint06\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 " #problem 2" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "k:=matrix([[3/2,1/2,-1,0],[1/2,1/2+
sqrt(2),0,0],[-1,0,3/2,-1/2],[0,0,-1/2,1/2+sqrt(2)]]);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"kGK%'matrixG6#7&7&#\"\"$\"\"##\"\"\"F,!\"\"\"
\"!7&F-,&F-F.*$F,F-F.F0F07&F/F0F*#F/F,7&F0F0F5F2Q(pprint06\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eigenvalues(k);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6&,(#\"\"\"\"\"#F%*&F&!\"\"F&F$F%*&F&F(\"\"$F$F%,
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0 "" {MPLTEXT 1 0 28 "p:=[0,py,0,py]; #load case a" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"pG7&\"\"!%#pyGF&F'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "u1:=linsolve(k,p);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%#u1GK%'vectorG6#7&,$*(\"#Y!\"\",&\"\"#F,*&\"\"&\"\"\"F.#F1F.F1F1%#p
yGF1F,,$**F0F1F+F,F-F1F3F1F1,$*(F+F,F-F1F3F1F1F4Q(pprint06\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "M:=matrix([[1/sqrt(2),1/sqr
t(2),0,0],[-1,0,1,0],[0,0,-1/sqrt(2),1/sqrt(2)],[0,sqrt(2),0,0],[0,0,0
,sqrt(2)]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MGK%'matrixG6#7'7&
,$*&\"\"#!\"\"F,#\"\"\"F,F/F*\"\"!F07&F-F0F/F07&F0F0,$*&F,F-F,F.F-F*7&
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{MPLTEXT 1 0 19 "F1:=multiply(M,u1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%#F1GK%'vectorG6#7',$**\"#B!\"\"\"\"##\"\"\"F-,&F-F,*&\"\"&F/F-F.F/
F/%#pyGF/F/,$*(F+F,F0F/F3F/F/F),$*,F2F/\"#YF,F-F.F0F/F3F/F/F6Q(pprint0
6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "F12:=factor(F1[1])*
EA/L;F23:=factor(F1[2])*EA/L;F34:=factor(F1[3])*EA/L;F25:=factor(F1[4]
)*EA/L;F36:=factor(F1[5])*EA/L;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$
F12G,$*.\"\"#\"\"\"\"#B!\"\",&*$F'#F(F'F(\"\"&F*F(%#pyGF(%#EAGF(%\"LGF
*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$F23G,$*,\"#B!\"\",&\"\"#F(*&
\"\"&\"\"\"F*#F-F*F-F-%#pyGF-%#EAGF-%\"LGF(F-" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$F34G,$*.\"\"#\"\"\"\"#B!\"\",&*$F'#F(F'F(\"\"&F*F(%#
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$F36G,$*.\"\"&\"\"\"\"#B!\"\",&*$\"
\"##F(F-F(F'F*F(%#pyGF(%#EAGF(%\"LGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "p:=[px,0,px,0]; #load case b" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"pG7&%#pxG\"\"!F&F'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "u2:=linsolve(k,p);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%#u2GK%'vectorG6#7&,$*(\"\"#!\"\",&*$F+#\"\"\"F+F0\"\"%F0F0%#pxGF0F0
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"> " 0 "" {MPLTEXT 1 0 19 "F1:=multiply(M,u2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#F1GK%'vectorG6#7',&**\"\"%!\"\"\"\"##\"\"\"F-,&*$F-F
.F/F+F/F/%#pxGF/F/*&F-F,F2F/F,\"\"!,&**F+F,F-F.F0F/F2F/F,*&F-F,F2F/F/,
$F2F,F2Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "F12
:=factor(F1[1])*EA/L;F23:=factor(F1[2])*EA/L;F34:=factor(F1[3])*EA/L;F
25:=factor(F1[4])*EA/L;F36:=factor(F1[5])*EA/L;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$F12G**\"\"##\"\"\"F&%#pxGF(%#EAGF(%\"LG!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$F23G\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$F34G,$**\"\"##\"\"\"F'%#pxGF)%#EAGF)%\"LG!\"\"F-" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$F25G,$*(%#pxG\"\"\"%#EAGF(%\"LG!\"
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