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"Help Variable" -1 25 "Courier" 0 1 0 0 0 1 2 2 0 2 2 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" -1 203 "" 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 "_pstyle1" -1 200 1 {CSTYLE "" -1 -1 "Courier" 0 1 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "_ps tyle2" -1 201 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 {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 11 "# Example 1" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 13 "with( linalg):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 39 "A:=matrix([[1,2,3],[2,-1,1],[3,0,-1]]);" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 19 "b:=vector([9,8,3]);" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 25 "print (\"(1)\"); inverse(A);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 30 "print(\"(2)\"); C:=augment(A,b);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 25 "print(\"(3)\"); R:=r ref(C);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 26 "print(\"(4)\"); X:=col(R,4);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 25 "print(\"(5)\"); evalm(A^3);" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 27 "print (\"(6)\"); transpose(A);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 31 "print(\"(7)\"); evalm(A-3*(A^2));" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 58 "print(\"(8)\"); \+ X:=linsolve(A,b); X:=evalm(inverse(A) &* b);" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 66 "print(\"(9)\"); F:=matrix( [[1,2,3],[2,-1,1],[0,0,0]]);linsolve(F,b);" }{MPLTEXT 1 0 58 "\n# Noth ing is printed, because of a signal equation \"0=3\"." }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 40 "print(\"(10)\"); evalm(transpose( A) &* A);" }{MPLTEXT 1 0 35 "\nevalm(inverse(transpose(A) &* A));" } {MPLTEXT 1 0 42 "\nevalm(inverse(A)&*transpose(inverse(A)));" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 11 "# Example 2" }{MPLTEXT 1 0 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 28 "A:=ma trix([[ 1, 1, 1, 2, 6]," }{MPLTEXT 1 0 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 0 28 " [ 2, 3,-2, 1,-3]," }{MPLTEXT 1 0 0 "" }} {PARA 200 "> " 0 "" {MPLTEXT 1 0 28 " [ 3, 5,-5, 1,-8]," } {MPLTEXT 1 0 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 0 30 " [ \+ 4, 3, 8, 2, 3]]);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 57 "print(\"(1)\"); C:=rref(A); # leading ones in columns 1,2,4" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 58 " BASIScolumnspace=col(A,1),col(A,2),col(A,4);" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 68 "print (\"(2)\"); F:=rref(transpose(A)); # leading ones in columns 1,2,3" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 55 " \+ BASISrowspace=row(A,1),row(A,2),row(A,3);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 58 "print(\"(3)\"); nullsp ace(A); linsolve(A,vector([0,0,0,0]));" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 54 "print(\"(4)\"); RANK=rank(A); NUL LITY=coldim(A)-rank(A);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 66 "print(\"(5)\"); DIMnullspace=coldim(A)-rank(A); D IMrowspace=rank(A);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 37 " DIMcolumnspace=rank(A);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 11 "# Example 3" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 28 "A:=matrix([[ 1 , 1, 1, 2, 6]," }{MPLTEXT 1 0 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 0 28 " [ 2, 3,-2, 1,-3]," }{MPLTEXT 1 0 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 0 28 " [ 3, 5,-5, 1,-8]," }{MPLTEXT 1 0 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 0 30 " [ 4, 3, 8, 2, 3]]); " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 41 "v1 :=col(A,1); v2:=col(A,2); v3:=col(A,4);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 53 "w1:=vector([1, 0, 0, -3]); w2:=ve ctor([0, 1, 0, 17]);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 26 "w3:=vector([0, 0, 1, -9]);" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 21 "F:=augment(v1,v2,v3);" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 21 "G:=au gment(w1,w2,w3);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 16 "H:=augment(F,G);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 26 "rank(F); rank(G); rank(H);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 41 "B:=rref(transpose(A)); # pivot co ls 1,2,3" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 41 "w1:=row(B,1); w2:=row(B,2); w3:=row(B,3);" }{MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 11 "# Example 4" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 38 "A:=matrix([[1,2,3],[2, -1,1],[3,0,0]]);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 52 "linsolve(evalm(A-(-3)*diag(1,1,1)),vector([0,0,0]));" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 27 "# a ns: t_1*vector([-2,1,2])" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 45 "# Basis == partial on t_1 == vector([-2,1,2])" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {PARA 201 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }