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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 14 "WORKED EXAMPLE" }}{PARA 
0 "" 0 "" {TEXT -1 30 "Consider the nonlinear system\n" }{OLE 1 4116 
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"" 0 "" {TEXT -1 29 "First load the package linalg" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 30 "Enter the equations as follows" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 10 "f:=-2*x+y;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 10 "g:=-y+x^2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "The equilib
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23 "solve(\{f=0,g=0\},\{x,y\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
41 "The equilibrium points are( , ) and ( , )" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 107 "To find the Jacobian matrix of the system of equation
s first represent the equations as a vector as follows" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "v:=[f,g];" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 26 "Use the \"jacobian\" command" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 21 "J:=jacobian(v,[x,y]);" }}{PARA 11 "" 1 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "At (0,0)  substitute  t
he coordinates" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "J00:=subs
(x=0,y=0,evalm(J));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "The linear
isation at (0,0) is therefore" }}{PARA 0 "" 0 "" {TEXT -1 21 "        \+
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{TEXT -1 22 "                      " }{OLE 1 4116 1 "[xm]Br=WfoRrB:::w
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