{VERSION 4 0 "IBM INTEL NT" "4.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{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 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "# Example 1" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "A:=matrix([[1,2,3],[2,-1,1],[3,0,-1
]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "b:=vector([9,8,3]);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "print(\"(1)\"); inverse
(A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "print(\"(2)\"); C:=
augment(A,b);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "print(\"(3
)\"); R:=rref(C);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "print(
\"(4)\"); X:=col(R,4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "p
rint(\"(5)\"); evalm(A^3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
27 "print(\"(6)\"); transpose(A);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "print(\"(7)\"); evalm(A-3*(A^2));" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 58 "print(\"(8)\"); X:=linsolve(A,b); X:=evalm(
inverse(A) &* b);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "# Example 2" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 28 "A:=matrix([[ 1, 1, 1, 2, 6]," }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 28 "           [ 2, 3,-2, 1,-3]," }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 28 "           [ 3, 5,-5, 1,-8]," }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "           [ 4, 3, 8, 2, 3]]);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 57 "print(\"(1)\"); C:=rref(A); # leading ones in \+
columns 1,2,4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "          \+
    BASIScolumnspace=col(A,1),col(A,2),col(A,4);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 68 "print(\"(2)\"); F:=rref(transpose(A)); # lead
ing ones in columns 1,2,3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
55 "              BASISrowspace=row(A,1),row(A,2),row(A,3);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "print(\"(3)\"); nullspace(A)
; linsolve(A,vector([0,0,0,0]));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 54 "print(\"(4)\"); RANK=rank(A); NULLITY=coldim(A)-rank(
A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "print(\"(5)\"); DIMn
ullspace=coldim(A)-rank(A); DIMrowspace=rank(A);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 37 "              DIMcolumnspace=rank(A);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 11 "# Example 3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "A:
=matrix([[ 1, 1, 1, 2, 6]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "     \+
      [ 2, 3,-2, 1,-3]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "        \+
   [ 3, 5,-5, 1,-8]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "           \+
[ 4, 3, 8, 2, 3]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "v1:=
col(A,1); v2:=col(A,2); v3:=col(A,4);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 53 "w1:=vector([1, 0, 0, -3]); w2:=vector([0, 1, 0, 17]);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "w3:=vector([0, 0, 1, -9
]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "F:=augment(v1,v2,v3)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "G:=augment(w1,w2,w3);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "H:=augment(F,G);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "rank(F); rank(G); rank(H);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 41 "B:=rref(transpose(A)); # pivot cols 1,2,3" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "w1:=row(B,1); w2:=row(B,2); \+
w3:=row(B,3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "# Example 4" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 38 "A:=matrix([[1,2,3],[2,-1,1],[3,0,0]]);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "linsolve(evalm(A-(-3)*diag(1
,1,1)),vector([0,0,0]));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 
"# ans: t_1*vector([-2,1,2])" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 45 "# Basis == partial on t_1 == vector([-2,1,2])" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 
1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }