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{SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT -1 0 "" }{TEXT 266 24 "Linear A
lgebra Powertool" }}{PARA 256 "" 0 "" {TEXT -1 40 "Solving a system by
 Gaussian Elimination" }}{PARA 0 "" 0 "" {TEXT 267 26 "Worksheet by Ru
ssell Blyth" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 263 64 "St
art linear algebra computations by loading the linalg package:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 256 41 "Enter the augmented matrix of the system
." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "A:=matrix([[-1,1,-1,-8
],[1,1,1,0],[2,4,8,-2]]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 258 99 "Let
's switch the first two rows to get a 1 as the (1,1) entry (we could a
lso multiply row 1 by -1)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
18 "B:=swaprow(A,1,2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 324 "Now a
dd suitable multiples of the first row to each of the second and third
 rows. Note that a colon instead of a semicolon suppresses printing th
e result of a command, which allows for multiple commands on one input
 line. Using the colon in the command with(linalg) would suppress the \+
list of commands in the linalg package." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "B:=addrow(B,1,2,1): B:=addrow(B,1,3,-2);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 259 96 "Multiply row 2 by 1/2 to get a leading 1
 in row 2 (note Maple does rational arithmetic exactly)." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "B:=mulrow(B,2,1/2);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 260 71 "Add a suitable multiple of row 2 to row \+
3 to clear out the (3,2) entry." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 20 "B:=addrow(B,2,3,-2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 19 "B:=mulrow(B,3,1/6);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 44 "Now
 solve the system using backsubstitution." }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 61 "Maple will autom
ate the process of row reducing even further:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 13 "gausselim(A);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
264 48 "Note that gausselim does not produce leading 1's" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "gaussjord(A);" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT 265 61 "The same result is given by rref (= reduced row e
chelon form)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "rref(A);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 2 0" 24 }
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