{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {PSTYLE "Dash Item" -1 16 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 3 }{PSTYLE "Wa rning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 2 2 1 0 0 0 1 }1 0 0 -1 -1 -1 2 0 2 0 2 2 -1 1 }{PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 2 }{PSTYLE "_pstyle4" -1 200 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }0 0 0 -1 -1 -1 2 0 2 0 2 2 -1 1 } {PSTYLE "_pstyle3" -1 201 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 0 255 1 0 0 0 2 2 1 0 0 0 1 }1 0 0 -1 -1 -1 2 0 2 0 2 2 -1 1 }{PSTYLE "_psty le2" -1 202 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }3 3 0 -1 -1 -1 2 0 2 0 2 2 -1 1 }{PSTYLE "_pstyle1" -1 203 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }0 0 0 -1 -1 -1 2 0 2 0 2 2 -1 1 }{PSTYLE "Line Printed Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 2 2 1 0 0 0 1 }1 0 0 -1 -1 -1 2 0 2 0 2 2 -1 1 } {PSTYLE "Heading 4" -1 20 1 {CSTYLE "" -1 -1 "Times" 1 10 0 0 0 1 1 1 2 2 2 2 0 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 0 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "T imes" 1 14 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }1 1 0 0 8 2 2 0 2 0 2 2 -1 1 } {PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }3 3 0 -1 -1 -1 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }1 1 0 0 8 4 2 0 2 0 2 2 -1 1 }{PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "T imes" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }3 1 0 0 8 8 2 0 2 0 2 2 -1 1 } {PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Help" -1 10 1 {CSTYLE "" -1 -1 "Courier" 1 9 0 0 255 1 0 0 0 2 2 1 0 0 0 1 }1 0 0 -1 -1 -1 2 0 2 0 2 2 -1 1 }{PSTYLE "Left Justified Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 3 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Fixed Width" -1 17 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 2 2 1 0 0 0 1 }1 0 0 -1 -1 -1 2 0 2 0 2 2 -1 1 } {PSTYLE "List Item" -1 14 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 5 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 0 255 1 0 0 0 2 2 1 0 0 0 1 }1 0 0 -1 -1 -1 2 0 2 0 2 2 -1 1 }{PSTYLE "Diagnostic" -1 9 1 {CSTYLE "" -1 -1 "Courier" 1 10 64 128 64 1 0 0 0 2 2 1 0 0 0 1 }1 0 0 -1 -1 -1 2 0 2 0 2 2 -1 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 0 0 0 1 }3 1 0 0 12 12 2 0 2 0 2 2 -1 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }0 0 0 -1 -1 -1 2 0 2 0 2 2 -1 1 }{PSTYLE "_pstyle12" -1 204 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }1 3 0 -1 -1 -1 2 0 2 0 2 2 -1 1 }{CSTYLE "LaTeX" -1 32 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }{CSTYLE "Maple Comment" -1 21 "Courier" 0 1 0 0 0 1 0 0 0 2 2 2 0 0 0 1 }{CSTYLE "2D Math Bold" -1 5 "Times" 0 1 0 0 0 0 0 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined" -1 44 "Times" 1 12 0 0 0 0 0 0 1 2 2 2 0 0 0 1 }{CSTYLE "Output Labels" -1 29 "Times" 1 8 0 0 0 1 0 0 0 2 2 2 0 0 0 1 }{CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }{CSTYLE "Page Number" -1 33 "Times" 0 1 0 0 0 0 0 0 2 2 2 2 0 0 0 1 }{CSTYLE "Text" -1 200 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small" -1 201 "Times" 0 1 0 0 0 0 1 0 2 2 2 2 0 0 0 1 }{CSTYLE "Help Heading" -1 26 "" 1 14 0 0 0 0 0 1 0 2 2 2 0 0 0 1 }{CSTYLE "Help Italic Bold" -1 40 "Times" 1 12 0 0 0 0 1 1 0 2 2 2 0 0 0 1 }{CSTYLE "Help Normal" -1 30 "Times" 1 12 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }{CSTYLE "Help Nonterminal" -1 24 "Courier" 0 1 0 0 0 1 0 1 0 2 2 2 0 0 0 1 }{CSTYLE "2D Math Small" -1 7 "Times" 0 1 0 0 0 0 0 0 2 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined Italic" -1 43 "T imes" 1 12 0 0 0 0 1 0 1 2 2 2 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 2 2 2 0 0 0 1 }{CSTYLE "Copyright" -1 34 "Times" 1 10 0 0 0 0 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 2 2 2 0 0 0 1 }{CSTYLE "Plot Title" -1 27 "" 1 10 0 0 0 0 0 1 0 2 2 2 0 0 0 1 }{CSTYLE "ParagraphStyle2" -1 202 "Times" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }{CSTYLE "2D Input" -1 19 "Times" 0 1 255 0 0 1 0 0 2 2 2 2 0 0 0 1 }{CSTYLE "ParagraphStyle1" -1 203 "Times" 0 1 0 0 255 1 0 0 2 2 2 2 0 0 0 1 }{CSTYLE "Help Maple Name" -1 35 "" 0 1 104 64 92 1 0 1 0 2 2 2 0 0 0 1 }{CSTYLE "Help Italic" -1 42 "Times" 1 12 0 0 0 0 1 0 0 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined Bold" -1 41 "Times" 1 12 0 0 0 0 0 1 1 2 2 2 0 0 0 1 }{CSTYLE "Default" -1 38 " " 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }{CSTYLE "Help Fixed" -1 23 "Courier " 1 10 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 0 1 0 0 255 1 0 0 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic" -1 3 "Time s" 0 1 0 0 0 0 1 0 2 2 2 2 0 0 0 1 }{CSTYLE "Popup" -1 31 "" 0 1 0 128 128 1 1 0 1 2 2 2 0 0 0 1 }{CSTYLE "2D Math Symbol 2" -1 204 "Time s" 0 1 0 0 0 0 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Plot Text" -1 28 "" 1 8 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }{CSTYLE "Help Notes" -1 37 "" 0 1 0 0 0 1 0 1 0 2 2 2 0 0 0 1 }{CSTYLE "Help Bold" -1 39 "Times" 1 12 0 0 0 0 0 1 0 2 2 2 0 0 0 1 }{CSTYLE "Help Menus" -1 36 "" 0 1 0 0 0 1 0 1 0 2 2 2 0 0 0 1 }{CSTYLE "_cstyle256" -1 205 "" 0 1 0 0 0 0 0 0 1 2 2 2 0 0 0 1 }{CSTYLE "2D Comment" -1 18 "Times" 0 1 0 0 0 0 0 0 2 2 2 2 0 0 0 1 }{CSTYLE "Help Variable" -1 25 "Courier" 0 1 0 0 0 1 2 2 0 2 2 2 0 0 0 1 }{CSTYLE "_cstyle5" -1 206 "Times" 0 1 0 0 0 0 0 0 1 2 2 2 0 0 0 1 }{CSTYLE "_cstyle4" -1 207 "Times" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }{CSTYLE "_cstyle3" -1 208 "Courier" 1 10 255 0 255 1 0 0 0 2 2 2 0 0 0 1 }{CSTYLE "_cstyle2" -1 209 "Times" 0 1 0 0 255 1 0 0 2 2 2 2 0 0 0 1 }{CSTYLE "_cstyle1" -1 210 "Courier" 0 1 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }{CSTYLE "2D Math Bold Small" -1 10 "Times" 0 1 0 0 0 0 0 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Emphasized" -1 211 "" 0 1 0 0 0 0 1 2 0 2 2 2 0 0 0 1 }{CSTYLE "Prompt" -1 1 "Courier" 0 1 0 0 0 1 0 0 0 2 2 2 0 0 0 1 }{PSTYLE "_pstyle5" -1 205 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }1 1 0 0 8 4 2 0 2 0 2 2 -1 1 }{PSTYLE "_pstyle6" -1 206 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }0 0 0 -1 -1 -1 2 0 2 0 2 2 -1 1 }{CSTYLE "_cstyle6" -1 212 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "_cstyle7" -1 213 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "_cstyle8" -1 214 "Courier" 0 1 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }{PSTYLE "_pstyle7" -1 207 1 {CSTYLE " " -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }0 0 0 -1 -1 -1 2 0 2 0 2 2 -1 1 }{CSTYLE "_cstyle9" -1 215 "Courier" 0 1 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }{PSTYLE "_pstyle8" -1 208 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 2 2 1 0 0 0 1 }1 0 0 -1 -1 -1 2 0 2 0 2 2 -1 1 } {CSTYLE "_cstyle10" -1 216 "Courier" 1 10 0 0 255 1 0 0 0 2 2 2 0 0 0 1 }{PSTYLE "_pstyle9" -1 209 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }3 3 0 -1 -1 -1 2 0 2 0 2 2 -1 1 }{CSTYLE "_cstyle11" -1 217 "Times" 0 1 0 0 255 1 0 0 2 2 2 2 0 0 0 1 }{PSTYLE "_pstyle10" -1 210 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }} {SECT 0 {SECT 1 {PARA 205 "" 0 "" {TEXT -1 31 "Matrix Manipulations wi th Maple" }}{PARA 206 "" 0 "" {TEXT 212 113 "Hello. Welcome to Maple's collection of linear algebra options. Some of these commands are in a library called " }{TEXT 213 13 "LinearAlgebra" }{TEXT 212 33 ", oth ers are in a library called " }{TEXT 213 6 "linalg" }{TEXT 212 67 ". \+ I can't keep track of what is in what so I load both libraries. " }} {PARA 206 "" 0 "" }{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 8 "restar t;" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 215 20 "with(LinearAlgebr a):" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 13 "with(linalg):" } }{PARA 208 "" 1 "" {TEXT 216 103 "Warning, the previous binding of the name GramSchmidt has been removed and it now has an assigned value" } {TEXT 216 1 "\n" }}{PARA 208 "" 1 "" {TEXT 216 79 "Warning, the protec ted names norm and trace have been redefined and unprotected" }{TEXT 216 1 "\n" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 215 40 "A1:= <<1,2 ,3,4>|<5,6,7,5>|<9,10,11,12>>;" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#>I# A1G6\"-I'RTABLEGF%6%\"'O$e&-I'MATRIXGF%6#7&7%\"\"\"\"\"&\"\"*7%\"\"#\" \"'\"#57%\"\"$\"\"(\"#67%\"\"%F0\"#7I'MatrixG6$I*protectedGF?I(_syslib GF%" }{TEXT 217 1 " " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 19 "A := Transpose(A1);" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#>I\"AG6\"-I'R TABLEGF%6%\"'W%)[-I'MATRIXGF%6#7%7&\"\"\"\"\"#\"\"$\"\"%7&\"\"&\"\"'\" \"(F47&\"\"*\"#5\"#6\"#7I'MatrixG6$I*protectedGF>I(_syslibGF%" }{TEXT 217 1 " " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 13 "b := <1,1,1 >;" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#>I\"bG6\"-I'RTABLEGF%6%\"'KUQ-I 'MATRIXGF%6#7%7#\"\"\"F.F.&I'VectorG6$I*protectedGF3I(_syslibGF%6#I'co lumnGF%" }{TEXT 217 1 " " }}}{EXCHG {PARA 206 "" 0 "" {TEXT 213 80 "Ho w do I solve the equation Ax = b for x? You can use the LinearSolve c ommand. " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 17 "LinearSolve (A,b);" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#-I'RTABLEG6\"6%\")'p)*)>-I' MATRIXGF%6#7&7#,&!\"\"\"\"\"&I$_t0GF%6#\"\"$F/7#,&F/F/F0!\"#7#F07#\"\" !&I'VectorG6$I*protectedGF=I(_syslibGF%6#I'columnGF%" }{TEXT 217 1 " " }}}{EXCHG {PARA 206 "" 0 "" {TEXT 213 126 "The _t03 is the free vari able. We get the general solution to the homogeneous equation and a pa rticular solution from this. " }{TEXT 212 1 " " }}}{EXCHG {PARA 206 " > " 0 "" {MPLTEXT 1 214 19 "xh := ;" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#>I#xhG6\"-I'RTABLEGF%6%\")%37.#-I'MATRIXGF%6#7&7#I\"tGF %7#,$F/!\"#F.7#\"\"!&I'VectorG6$I*protectedGF8I(_syslibGF%6#I'columnGF %" }{TEXT 217 1 " " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 18 "x p := <-1,1,0,0>; " }}{PARA 209 "" 1 "" {XPPMATH 20 "6#>I#xpG6\"-I'RTAB LEGF%6%\"(G]<\"-I'MATRIXGF%6#7&7#!\"\"7#\"\"\"7#\"\"!F2&I'VectorG6$I*p rotectedGF7I(_syslibGF%6#I'columnGF%" }{TEXT 217 1 " " }}}{EXCHG {PARA 206 "" 0 "" {TEXT 212 25 "Here, xh is the general s" }{TEXT 212 47 "olution to the homogeneous equation. Check it. " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 15 "Multiply(A,xh);" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#-I'RTABLEG6\"6%\")o2X?-I'MATRIXGF%6#7%7#\"\"!F,F,&I'Vec torG6$I*protectedGF1I(_syslibGF%6#I'columnGF%" }{TEXT 217 1 " " }}} {EXCHG {PARA 206 "" 0 "" {TEXT 212 75 "And, xp is a particular solutio n found by setting _tO3 to zero. Check it. " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 15 "Multiply(A,xp);" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#-I'RTABLEG6\"6%\"'Kz]-I'MATRIXGF%6#7%7#\"\"\"F,F,&I'Vec torG6$I*protectedGF1I(_syslibGF%6#I'columnGF%" }{TEXT 217 1 " " }}} {EXCHG {PARA 206 "" 0 "" {TEXT 212 197 "You would suppose that since t he homogeneous solution has one free parameter, then the nullity would be equal to one. Since there are four columns this would imply that \+ the rank = 3. Let's check. " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 8 "rank(A);" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#\"\"$" }{TEXT 217 1 " " }}}{EXCHG {PARA 206 "" 0 "" {TEXT 212 20 "Wow. We were right. " }}}{EXCHG {PARA 206 "" 0 "" {TEXT 213 55 "What about square matrices, \+ inverses and determinants? " }{TEXT 212 17 "\nGlad you asked. " }}} {EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 8 "restart;" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 20 "with(LinearAlgebra):" }}} {EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 13 "with(linalg):" }}{PARA 208 "" 1 "" {TEXT 216 103 "Warning, the previous binding of the name G ramSchmidt has been removed and it now has an assigned value" }{TEXT 216 1 "\n" }}{PARA 208 "" 1 "" {TEXT 216 79 "Warning, the protected na mes norm and trace have been redefined and unprotected" }{TEXT 216 1 " \n" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 31 "A := <<1,2,3>|<4, 5,6>|<2,1,2>>;" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#>I\"AG6\"-I'RTABLEG F%6%\")77**>-I'MATRIXGF%6#7%7%\"\"\"\"\"%\"\"#7%F1\"\"&F/7%\"\"$\"\"'F 1I'MatrixG6$I*protectedGF9I(_syslibGF%" }{TEXT 217 1 " " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 15 "Determinant(A);" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#!\"'" }{TEXT 217 1 " " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 17 "MatrixInverse(A);" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#-I'RTABLEG6\"6%\")Ss$Q#-I'MATRIXGF%6#7%7%#!\"#\"\"$F-\" \"\"7%#F0\"\"'#\"\"#F/#!\"\"F57%#F0F5F7F9I'MatrixG6$I*protectedGF " 0 "" {MPLTEXT 1 214 29 "Multiply(MatrixInverse(A),A);" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#-I'RTABLEG6\"6%\")KS2B-I'MATRIXGF%6#7%7%\"\"\"\"\"!F.7%F.F-F.7%F .F.F-I'MatrixG6$I*protectedGF3I(_syslibGF%" }{TEXT 217 1 " " }}} {EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 13 "b := <1,1,1>;" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#>I\"bG6\"-I'RTABLEGF%6%\")G " 0 " " {MPLTEXT 1 214 25 "sol1 := LinearSolve(A,b);" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#>I%sol1G6\"-I'RTABLEGF%6%\"))y(GB-I'MATRIXGF%6#7%7##!\" \"\"\"$7##\"\"\"F17#\"\"!&I'VectorG6$I*protectedGF:I(_syslibGF%6#I'col umnGF%" }{TEXT 217 1 " " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 37 "sol2 := Multiply(MatrixInverse(A),b);" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#>I%sol2G6\"-I'RTABLEGF%6%\")G3GB-I'MATRIXGF%6#7%7##!\" \"\"\"$7##\"\"\"F17#\"\"!&I'VectorG6$I*protectedGF:I(_syslibGF%6#I'col umnGF%" }{TEXT 217 1 " " }}}{EXCHG {PARA 206 "" 0 "" {TEXT 212 32 "It \+ Worked! Check your answers. " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 21 "Multiply(A,sol1) - b;" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#-I 'RTABLEG6\"6%\")g#[P#-I'MATRIXGF%6#7%7#\"\"!F,F,&I'VectorG6$I*protecte dGF1I(_syslibGF%6#I'columnGF%" }{TEXT 217 1 " " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 21 "Multiply(A,sol2) - b;" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#-I'RTABLEG6\"6%\"'Gk]-I'MATRIXGF%6#7%7#\"\"!F,F,&I'Vect orG6$I*protectedGF1I(_syslibGF%6#I'columnGF%" }{TEXT 217 1 " " }}} {EXCHG {PARA 206 "" 0 "" {TEXT 212 279 "There are many other fun thing s we can do with Maple but we will stop here for two reasons. One we' ll do more later in the semester. Two, we are in the process of gettin g Maple 10 which is drastically different that Maple 9 and much of thi s rigorous syntax will be unnecessary. " }}}}{SECT 1 {PARA 205 "" 0 "" {TEXT -1 54 "Who put the algebra in Computer Algebra System (CAS)? " }}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 8 "restart;" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 20 "with(LinearAlgebra):" }}} {EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 13 "with(linalg):" }}{PARA 208 "" 1 "" {TEXT 216 103 "Warning, the previous binding of the name G ramSchmidt has been removed and it now has an assigned value" }{TEXT 216 1 "\n" }}{PARA 208 "" 1 "" {TEXT 216 79 "Warning, the protected na mes norm and trace have been redefined and unprotected" }{TEXT 216 1 " \n" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 42 "A := Transpose(<< a,b,c>|<0,e,f>|<0,0,j>>);" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#>I\"AG6 \"-I'RTABLEGF%6%\")+?%Q#-I'MATRIXGF%6#7%7%I\"aGF%I\"bGF%I\"cGF%7%\"\"! I\"eGF%I\"fGF%7%F3F3I\"jGF%I'MatrixG6$I*protectedGF:I(_syslibGF%" } {TEXT 217 1 " " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 15 "Deter minant(A);" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#*(I\"aG6\"\"\"\"I\"eGF% F&I\"jGF%F&" }{TEXT 217 1 " " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 17 "MatrixInverse(A);" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#-I'RTA BLEG6\"6%\")_S:@-I'MATRIXGF%6#7%7%*$I\"aGF%!\"\",$*(I\"bGF%\"\"\"F.F/I \"eGF%F/F/**,&*&F2F3I\"fGF%F3F3*&F4F3I\"cGF%F3F/F3F.F/F4F/I\"jGF%F/7% \"\"!*$F4F/,$*(F8F3F4F/F;F/F/7%F=F=*$F;F/I'MatrixG6$I*protectedGFEI(_s yslibGF%" }{TEXT 217 1 " " }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 35 "Id := Multiply(MatrixInverse(A),A);" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#>I#IdG6\"-I'RTABLEGF%6%\")'*39>-I'MATRIXGF%6#7%7%\"\"\" \"\"!,(*&I\"aGF%!\"\"I\"cGF%F/F/**I\"bGF%F/F3F4I\"eGF%F4I\"fGF%F/F4*(, &*&F7F/F9F/F/*&F8F/F5F/F4F/F3F4F8F4F/7%F0F/F07%F0F0F/I'MatrixG6$I*prot ectedGFBI(_syslibGF%" }{TEXT 217 1 " " }}}{EXCHG {PARA 206 "" 0 "" {TEXT 212 90 "Is that the identity matrix? Sure is. Can we get Maple \+ to interpret it as such? Sure Can." }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 214 13 "simplify(Id);" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#- I'RTABLEG6\"6%\"'s:M-I'MATRIXGF%6#7%7%\"\"\"\"\"!F.7%F.F-F.7%F.F.F-I'M atrixG6$I*protectedGF3I(_syslibGF%" }{TEXT 217 1 " " }}}}{PARA 210 "" 0 "" }}{VIEWOPTS 1 1 0 1 1 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 } {RTABLE_HANDLES 23842000 21154052 19140896 341572 }{RTABLE M7R0 I5RTABLE_SAVE/23842000X,%)anythingG6"6"[gl!"%!!!#*"$"$%"aG""!F(%"bG%"eGF(%"cG%" fG%"jGF& } {RTABLE M7R0 I5RTABLE_SAVE/21154052X,%)anythingG6"6"[gl!"%!!!#*"$"$*$%"aG!""""!F*,$*(%"bG""" F(F)%"eGF)F)*$F/F)F***,&*&F-F.%"fGF.F.*&F/F.%"cGF.F)F.F(F)F/F)%"jGF),$*(F4F.F/F )F7F)F)*$F7F)F& } {RTABLE M7R0 I5RTABLE_SAVE/19140896X,%)anythingG6"6"[gl!"%!!!#*"$"$"""""!F(F(F'F(,(*&%"aG!"" %"cGF'F'**%"bGF'F+F,%"eGF,%"fGF'F,*(,&*&F/F'F1F'F'*&F0F'F-F'F,F'F+F,F0F,F'F(F'F & } {RTABLE M7R0 I3RTABLE_SAVE/341572X,%)anythingG6"6"[gl!"%!!!#*"$"$"""""!F(F(F'F(F(F(F'F& }