{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "#3.2-14 solved with \+ maple" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "A1:=matrix([[3,-6,-2,1],[2,- 4,1,17],[1,-2,-2,-9]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1GK%'ma trixG6#7%7&\"\"$!\"'!\"#\"\"\"7&\"\"#!\"%F-\"#<7&F-F,F,!\"*Q(pprint06 \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "# last frame in one s tep" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "rref(A1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7%7&\"\"\"!\"#\"\"!\"\"&7&F*F*F( \"\"(7&F*F*F*F*Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "# Frame sequence A1, A2, A3, A4, ..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "A2:=swaprow(A1,1,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A2GK%'matrixG6#7%7&\"\"\"!\"#F+!\"*7&\"\"#!\"%F*\"#<7&\"\"$!\"'F +F*Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "A3:=addr ow(A2,1,2,-2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A3GK%'matrixG6#7% 7&\"\"\"!\"#F+!\"*7&\"\"!F.\"\"&\"#N7&\"\"$!\"'F+F*Q(pprint06\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "A4:=addrow(A3,1,3,-3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A4GK%'matrixG6#7%7&\"\"\"!\"#F+!\"* 7&\"\"!F.\"\"&\"#N7&F.F.\"\"%\"#GQ(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "# Col 1 is the first col of the identity matrix " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "# Proceed to make col \+ 3 the second col of the \n# identity matrix. Then the last frame is fo und\n# which should equal rref(A1)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "# make a leading 1 in row 2\nA5:=addrow(A4,3,2,-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A5GK%'matrixG6#7%7&\"\"\"!\"#F+! \"*7&\"\"!F.F*\"\"(7&F.F.\"\"%\"#GQ(pprint06\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 22 "A6:=addrow(A5,2,3,-4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A6GK%'matrixG6#7%7&\"\"\"!\"#F+!\"*7&\"\"!F.F*\"\"(7 &F.F.F.F.Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "A7 :=addrow(A6,2,1,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A7GK%'matrix G6#7%7&\"\"\"!\"#\"\"!\"\"&7&F,F,F*\"\"(7&F,F,F,F,Q(pprint06\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "# last frame test passes\nrr ef(A1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7%7&\"\"\"!\"# \"\"!\"\"&7&F*F*F(\"\"(7&F*F*F*F*Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 131 "# To finish the solution, translate to equation s\n# and apply the Last Frame Algorithm.\n# This part of the solution \+ is done by hand." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG }{EXCHG }}{MARK "16 0 0" 0 }{VIEWOPTS 1 1 0 2 1 1805 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }