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{SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT 258 8 "Inverses" }}{PARA 258 "
" 0 "" {TEXT 256 4 "HW 2" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 257 "" 0 "" {TEXT -1 260 "Click on a [+]  sign to expand a secti
on. Click on a [-] sign to collapse a section. To do these exercises y
ou will have to insert execution groups. That can be done by clicking \+
on the toolbar icon that looks like \"[>\". It can also be done via th
e Insert menu." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 278 20 "Student Name and ID:" }}
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}{TEXT -1 3 "   " }{HYPERLNK 17 "worksheet" 2 "worksheet" "" }{TEXT 
-1 95 ",  you will be asked to perform calculations with inverses of m
atrices and elementary matrices." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 
8 "Keywords" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 60 " Clicking on any of these words will bring up its help page." }
}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 15 "" 0 "" {TEXT -1 3 "   " }
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ntaryMatricesR4.mws" 1 "elementaryMatricesR4.mws" "" }{TEXT -1 4 "    \+
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 36 "Calcu
late the inverse matrix of     " }{XPPEDIT 19 1 "MATRIX([[0, 0, 1, 1],
 [1, 0, 1, 0], [2, 3, 0, -4], [-1, 2, 0, 0]])" "-%'MATRIXG6#7&7&\"\"!F
'\"\"\"F(7&F(F'F(F'7&\"\"#\"\"$F',$\"\"%!\"\"7&,$F(F/F+F'F'" }{TEXT 
-1 116 "     by augmenting it with the identity matrix and obtaining t
he reduced row echelon form of the augmented matrix.  " }}{PARA 0 "" 
0 "" {TEXT -1 11 "           " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
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{TEXT -1 34 "Calculate the inverse matrix of   " }{XPPEDIT 19 1 "MATRI
X([[2, 0, 3], [1, 2, 0], [1, 1, 1]])" "-%'MATRIXG6#7%7%\"\"#\"\"!\"\"$
7%\"\"\"F'F(7%F+F+F+" }{TEXT -1 54 "   by writing it as a product of e
lementary matrices. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 260 "
" 0 "" {TEXT -1 11 "Exercise 3 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 27 "Background worksheet:      " }{HYPERLNK 
17 "elementaryMatricesR4.mws" 1 "elementaryMatricesR4.mws" "" }{TEXT 
-1 2 "  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
31 "Find the LU Decomposition of   " }{XPPEDIT 19 1 "MATRIX([[1, 2, 3,
 4], [0, 1, 1, 1], [1, 1, 1, 0], [0, 1, 2, 3]])" "-%'MATRIXG6#7&7&\"\"
\"\"\"#\"\"$\"\"%7&\"\"!F'F'F'7&F'F'F'F,7&F,F'F(F)" }{TEXT -1 2 " ." }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 10 "
Exercise 4" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 25 "Background worksheet:    " }{HYPERLNK 17 "elementaryMatricesR4.
mws" 1 "elementaryMatricesR4.mws" "" }{TEXT -1 2 "  " }}{PARA 0 "" 0 "
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{TEXT -1 6 "Let   " }{XPPEDIT 19 1 "A =MATRIX([[1, 2, 3, 4], [0, 1, 1,
 1], [1, 1, 1, 0], [0, 1, 2, 3]])" "/%\"AG-%'MATRIXG6#7&7&\"\"\"\"\"#
\"\"$\"\"%7&\"\"!F)F)F)7&F)F)F)F.7&F.F)F*F+" }{TEXT -1 1 "." }}{PARA 
0 "" 0 "" {TEXT -1 117 "\nUse the LU decomposition of the given matrix
 (calculated in Exercise 3) to solve the system\n\n                   \+
    " }{XPPEDIT 19 1 "MATRIX([[1, 2, 3, 4], [0, 1, 1, 1], [1, 1, 1, 0]
, [0, 1, 2, 3]])*MATRIX( [ [x[1]],[x[2]],[x[3]],[x[4]]]   )=MATRIX( [ \+
[2],[2],[-3],[8] ]  )" "/*&-%'MATRIXG6#7&7&\"\"\"\"\"#\"\"$\"\"%7&\"\"
!F)F)F)7&F)F)F)F.7&F.F)F*F+F)-F%6#7&7#&%\"xG6#F)7#&F66#F*7#&F66#F+7#&F
66#F,F)-F%6#7&7#F*7#F*7#,$F+!\"\"7#\"\")" }{TEXT -1 3 "  ." }}{PARA 0 
"" 0 "" {TEXT -1 12 "         \n  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 32 "Copyright and Author Information
" }}{EXCHG {PARA 261 "" 0 "" {TEXT -1 49 "309F03hw2R4.mws     A MapleV
 Release 4 worksheet." }}{PARA 262 "" 0 "" {TEXT -1 0 "" }}{PARA 263 "
" 0 "" {TEXT -1 44 "Author:  Brian E. Blank  (20 September 2003)" }}
{PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "This do
cument may not be distributed by any medium," }}{PARA 0 "" 0 "" {TEXT 
-1 55 "including print, disk, and electronic transfer, without" }}
{PARA 0 "" 0 "" {TEXT -1 39 "prior written permission of the author." 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 265 "" 0 "" {TEXT -1 49 "For m
ore information,  please contact the author:" }}{PARA 266 "" 0 "" 
{TEXT -1 4 "    " }}{PARA 266 "" 0 "" {TEXT -1 32 "     Department of \+
Mathematics, " }}{PARA 0 "" 0 "" {TEXT -1 39 "     Washington Universi
ty in St. Louis" }}{PARA 0 "" 0 "" {TEXT -1 26 "     St. Louis, MO   6
3130" }}{PARA 0 "" 0 "" {TEXT -1 3 "   " }}{PARA 0 "" 0 "" {TEXT -1 
33 "     Telephone:    (314) 935-6763" }}{PARA 267 "" 0 "" {TEXT -1 
44 "             e-mail:    brian@math.wustl.edu" }}{PARA 268 "" 0 "" 
{TEXT -1 0 "" }}{PARA 269 "" 0 "" {TEXT -1 56 "Copyright:  \251 2003 B
rian E. Blank,  All Rights Reserved." }}}}}{MARK "4 4 2" 113 }
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