{VERSION 3 0 "APPLE_PPC_MAC" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {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 } {VIEWOPTS 1 1 0 1 1 1803 }