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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 11 "Math 2250-3" }}{PARA 
257 "" 0 "" {TEXT -1 18 "September 18, 2000" }}{PARA 258 "" 0 "" 
{TEXT -1 20 "Maple linear algebra" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "with(linalg): #load linear a
lgebra package" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected \+
names norm and trace have been redefined and unprotected\n" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 21 "Problem #20, page 160" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 79 "A:= matrix(3,5,[2,4,-1,-2,2,1,3,2,-7,3,5,8,
-7,6,1]);\n   #the coefficient matrix" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%\"AG-%'matrixG6#7%7'\"\"#\"\"%!\"\"!\"#F*7'\"\"\"\"\"$F*!\"(F07'
\"\"&\"\")F1\"\"'F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "b:=v
ector([6,9,4]);  #the right hand side" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%\"bG-%'vectorG6#7%\"\"'\"\"*\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 90 "Aaugb:=augment(A,b);  #the augmented matrix...\n   #y
ou could have entered it directly too." }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%&AaugbG-%'matrixG6#7%7(\"\"#\"\"%!\"\"!\"#F*\"\"'7(\"\"\"\"\"$
F*!\"(F1\"\"*7(\"\"&\"\")F2F.F0F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 "rref(Aaugb);  #compute the reduced row echelon form" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7(\"\"\"\"\"!F)F)!\"$
\"\"#7(F)F(F)!\"\"F+F(7(F)F)F(!\"#F)F+" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 234 "From rref(Aaugb) you can read off the solution to the or
iginal problem.  Each column (from A) without a leading 1 gives you a \+
free parameter in the solution.  so we see x5=t, x4=s, x3=2+2s, x2=1+s
-2t, x1=2+3t is the general solution. " }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "linsolve(A,b);  #Maple'
s solution, looks different is\n  #really the same." }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%'vectorG6#7',(#\"\"(\"\"#\"\"\"*&#\"\"$F*F+&%#_tG6#
F*F+!\"\"*&#F.F*F+&F06#F+F+F+F/,&F*F+*&F*F+F5F+F+F5,(#F+F*F+*&#F+F*F+F
/F+F2*&F:F+F5F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "b1:=ve
ctor([0,0,0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#b1G-%'vectorG6#7%
\"\"!F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "linsolve(A,b1)
;  #solve the homogeneous problem" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-
%'vectorG6#7',$&%#_tG6#\"\"#\"\"$,&&F)6#\"\"\"F0*&F+F0F(F0!\"\",$F.F+F
.F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "rref(A);  #or read o
ff the solution from rref(A) directly." }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#-%'matrixG6#7%7'\"\"\"\"\"!F)F)!\"$7'F)F(F)!\"\"\"\"#7'F)F)F(!\"
#F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "13 0 0" 
58 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }