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"macro(swap=linalg [swaprow]);macro(mult=linalg[mulrow]);\nmacro(combo=linalg[addrow]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%I%swapG6\"I%multGF$I&comboGF$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%I%swapG6\"I%multGF$I&comboGF$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%I%swapG6\"I%multGF$I&comboGF$" }}} {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 "-I'MatrixG6$% *protectedGI(_syslibG6\"6#/I$%idGF'\"*kB8n\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "# last frame in one step" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "linalg[rref](A1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"\"\"$;F&\"\"%E\\[l-6$F&F'\"\"!6$F'F&F,6$F&\"\"#!\"#6$ F'F/F,6$F&F&F&6$F'F)F,6$F/F&F,6$F/F/F,6$F/F)\"\"(6$F'F'F,6$F/F'F&6$F&F )\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "# Frame sequence \+ A1, A2, A3, A4, ..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "A2:= swap(A1,1,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"\"\"$;F&\" \"%E\\[l-6$F&F'!\"#6$F'F&F'6$F&\"\"#F,6$F'F/!\"'6$F&F&F&6$F'F)F&6$F/F& F/6$F/F/!\"%6$F/F)\"#<6$F'F'F,6$F/F'F&6$F&F)!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "A3:=combo(A2,1,2,-2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"\"\"$;F&\"\"%E\\[l-6$F&F'!\"#6$F'F&F'6$F&\" \"#F,6$F'F/!\"'6$F&F&F&6$F'F)F&6$F/F&\"\"!6$F/F/F56$F/F)\"#N6$F'F'F,6$ F/F'\"\"&6$F&F)!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "A4:= combo(A3,1,3,-3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"\"\"$; F&\"\"%E\\[l-6$F&F'!\"#6$F'F&\"\"!6$F&\"\"#F,6$F'F0F.6$F&F&F&6$F'F)\"# G6$F0F&F.6$F0F0F.6$F0F)\"#N6$F'F'F)6$F0F'\"\"&6$F&F)!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "# Col 1 is the first col of the ide ntity matrix" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "# Proceed t o make col 3 the second col of the \n" }{MPLTEXT 1 0 48 "# identity ma trix. Then the last frame is found\n" }{MPLTEXT 1 0 29 "# which should equal rref(A1)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "# make a leading 1 in row 2\n" }{MPLTEXT 1 0 21 "A5:=combo(A4,3,2,-1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"\"\"$;F&\"\"%E\\[l-6$F&F'! \"#6$F'F&\"\"!6$F&\"\"#F,6$F'F0F.6$F&F&F&6$F'F)\"#G6$F0F&F.6$F0F0F.6$F 0F)\"\"(6$F'F'F)6$F0F'F&6$F&F)!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "A6:=combo(A5,2,3,-4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"\"\"$;F&\"\"%E\\[l-6$F&F'!\"#6$F'F&\"\"!6$F&\"\"#F,6$F' F0F.6$F&F&F&6$F'F)F.6$F0F&F.6$F0F0F.6$F0F)\"\"(6$F'F'F.6$F0F'F&6$F&F)! \"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "A7:=combo(A6,2,1,2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"\"\"$;F&\"\"%E\\[l-6$F& F'\"\"!6$F'F&F,6$F&\"\"#!\"#6$F'F/F,6$F&F&F&6$F'F)F,6$F/F&F,6$F/F/F,6$ F/F)\"\"(6$F'F'F,6$F/F'F&6$F&F)\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "# last frame test passes\nlinalg[" }{MPLTEXT 1 0 10 " rref](A1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"\"\"$;F&\"\"% E\\[l-6$F&F'\"\"!6$F'F&F,6$F&\"\"#!\"#6$F'F/F,6$F&F&F&6$F'F)F,6$F/F&F, 6$F/F/F,6$F/F)\"\"(6$F'F'F,6$F/F'F&6$F&F)\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "# To finish the solution, translate to equation s\n" }{MPLTEXT 1 0 38 "# and apply the Last Frame Algorithm.\n" } {MPLTEXT 1 0 44 "# This part of the solution is done by hand." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "# Answer check\nA:=Matrix([[ 3,-6,-2],[2,-4,1],[1,-2,-2]]);" }{MPLTEXT 1 0 5 "\nb:=<" }{MPLTEXT 1 0 9 "1,17,-9>;" }{MPLTEXT 1 0 56 "\nlinalg[linsolve](A,b);\nLinearAlge bra[LinearSolve](A,b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I'MatrixG6$%* protectedGI(_syslibG6\"6#/I$%idGF'\"*oC@z\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I'VectorG6$%*protectedGI(_syslibG6\"6#I'columnGF(6#/I$% idGF(\"*WQKz\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6#;\"\"\"\"\"$E\\[ l$F&,&\"\"&F&&I#_tGF#6#F&\"\"#F.F+F'\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I'VectorG6$%*protectedGI(_syslibG6\"6#I'columnGF(6#/I$% idGF(\"*WQut\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 2 1 1805 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }