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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 128 "Below is \+
a Maple worksheet that will allow you to see the effects of any 2-dime
nsional linear transformation on the unit square." }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }{TEXT 257 100 "First, you must load the linear a
lgebra package by clicking on the line below and hitting [return]. " }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 258 119 "Next, enter the procedur
e into the computer's memory, by clicking anywhere on the paragraph be
low and hitting [return]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
442 "with(plots):\nLinTrans := proc(T) local P,PT,plot1,plot2;\nP:=tra
nspose(matrix([ [0,0],[0,1],[1,1],[1,0],[0,0]])):\nPT:=multiply(T,P):
\nplot1:= plot( [convert(col(PT,1),list),\n       convert(col(PT,2),li
st),\n       convert(col(PT,3),list),\n       convert(col(PT,4),list),
\n       convert(col(PT,5),list)], scaling=constrained, color=red):\np
lot2:= plot( [[0,0],[0,1],[1,1],[1,0],[0,0] ], scaling=constrained, co
lor=blue):\ndisplay(plot1,plot2);\nend;" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }{TEXT 259 332 "To use this procedure, first enter the t
wo-dimensional matrix you want to use, and name it T, then plug the ma
trix T into the function LinTrans.  The example below shows the effect
s of multiplying by the matrix [ [cos(Pi/3), -sin(Pi/3)], [sin(Pi/3), \+
cos(Pi/3)] ] on the unit square.  Click anywhere on the paragraph belo
w to see it." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "T:= matrix(
 [ [cos(Pi/3), -sin(Pi/3)],[sin(Pi/3), cos(Pi/3)]]);\nLinTrans(T);" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 260 17 "Now you try it!  \+
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "7 0 1" 17 }
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