{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 "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }
{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 "" 0 256 1 {CSTYLE "
" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 
0 -1 0 }}
{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 42 "Spaces of vectors assoc
iated with a matrix" }}{PARA 0 "" 0 "" {TEXT -1 175 "Here are a few ex
amples of how you can use Maple to find the reduced row exhelon form o
f a matrix and to obtain bases in the Row space, Column space and Null
space of a matrix." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(
LinearAlgebra);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "A:=Matri
x([[1,4,5,6,9],[3,-2,1,4,-1],[-1,0,-1,-2,-1],[2,3,5,7,8]]);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "ReducedRowEchelonForm(A);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "NullSpace(A);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "RowSpace(A);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 15 "ColumnSpace(A);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 118 "You can also find the rank of the matrix, which is nothi
ng but the common dimension of the row and column spaces of A." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "Rank(A);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "10" 0 }{VIEWOPTS 1 1 0 1 1 1803 
1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }