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{TEXT -1 33 "LUDecomposition:   reducing row 1" }}{PARA 6 "" 1 "" 
{TEXT -1 36 "LUDecomposition:   looking for pivot" }}{PARA 6 "" 1 "" 
{TEXT -1 59 "LUDecomposition:   found new row.  Rank is 1.  nulldim is
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{PARA 6 "" 1 "" {TEXT -1 36 "LUDecomposition:   looking for pivot" }}
{PARA 6 "" 1 "" {TEXT -1 59 "LUDecomposition:   found new row.  Rank i
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or pivot" }}{PARA 6 "" 1 "" {TEXT -1 59 "LUDecomposition:   found new \+
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-1 32 "LUDecomposition:   reducing rows" }}{PARA 6 "" 1 "" {TEXT -1 
33 "LUDecomposition:   reducing row 5" }}{PARA 6 "" 1 "" {TEXT -1 36 "
LUDecomposition:   looking for pivot" }}{PARA 6 "" 1 "" {TEXT -1 59 "L
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"" 1 "" {TEXT -1 32 "LUDecomposition:   reducing rows" }}{PARA 6 "" 1 
"" {TEXT -1 33 "LUDecomposition:   reducing row 6" }}{PARA 6 "" 1 "" 
{TEXT -1 36 "LUDecomposition:   looking for pivot" }}{PARA 6 "" 1 "" 
{TEXT -1 37 "LUDecomposition:   done row reduction" }}{PARA 6 "" 1 "" 
{TEXT -1 42 "LUDecomposition:   generating pivot Matrix" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*gGk_\"-%'MATRIXG6#7'7(!#;!#\")!#)
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BLEG6%\"*+Rk_\"-%'MATRIXG6#7(7'!#;!\"*!#]!#A\"#X7'\"\"!#\"$@\"\"#;#\"%
\")=\"\")#\"%(e\"F8#!%<JF57'F2F2#\"&x9\"\"#6#\"&.!*)F4#!')y7\"F47'F2F2
#\"&%f7F@#\"'7;5F4#!'!*f7F47'F2F2#!%y(*F@#!&DQ)F4#\"'!z,\"F47'F2F2#!%a
%*F@#!&ck*F4#\"'yU5F4%'MatrixG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%3Se
arching~column~3G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%3Added~row~3~tim
es~G#!&%f7\"&x9\"%*~to~row~4G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RT
ABLEG6%\"*+Rk_\"-%'MATRIXG6#7(7'!#;!\"*!#]!#A\"#X7'\"\"!#\"$@\"\"#;#\"
%\")=\"\")#\"%(e\"F8#!%<JF57'F2F2#\"&x9\"\"#6#\"&.!*)F4#!')y7\"F47'F2F
2F2#\"(Az6%\"'Zi7#!(y8K#FH7'F2F2#!%y(*F@#!&DQ)F4#\"'!z,\"F47'F2F2#!%a%
*F@#!&ck*F4#\"'yU5F4%'MatrixG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%3Add
ed~row~3~times~G#\"%y(*\"&x9\"%*~to~row~5G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'RTABLEG6%\"*+Rk_\"-%'MATRIXG6#7(7'!#;!\"*!#]!#A\"#X7
'\"\"!#\"$@\"\"#;#\"%\")=\"\")#\"%(e\"F8#!%<JF57'F2F2#\"&x9\"\"#6#\"&.
!*)F4#!')y7\"F47'F2F2F2#\"(Az6%\"'Zi7#!(y8K#FH7'F2F2F2#!(\"QW$)FH#\"(1
d%fFH7'F2F2#!%a%*F@#!&ck*F4#\"'yU5F4%'MatrixG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6%%3Added~row~3~times~G#\"%a%*\"&x9\"%*~to~row~6G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*+Rk_\"-%'MATRIXG6#7(7'!
#;!\"*!#]!#A\"#X7'\"\"!#\"$@\"\"#;#\"%\")=\"\")#\"%(e\"F8#!%<JF57'F2F2
#\"&x9\"\"#6#\"&.!*)F4#!')y7\"F47'F2F2F2#\"(Az6%\"'Zi7#!(y8K#FH7'F2F2F
2#!(\"QW$)FH#\"(1d%fFH7'F2F2F2#!)]Y9CFH#\")9P'=\"FH%'MatrixG" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%3Searching~column~4G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6%%3Added~row~4~times~G#\"(\"QW$)\"(Az6%%*~to~row~5G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*+Rk_\"-%'MATRIXG6#7(7'!
#;!\"*!#]!#A\"#X7'\"\"!#\"$@\"\"#;#\"%\")=\"\")#\"%(e\"F8#!%<JF57'F2F2
#\"&x9\"\"#6#\"&.!*)F4#!')y7\"F47'F2F2F2#\"(Az6%\"'Zi7#!(y8K#FH7'F2F2F
2F2#\")J>D?\"(h*e?7'F2F2F2#!)]Y9CFH#\")9P'=\"FH%'MatrixG" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6%%3Added~row~4~times~G#\")DB27\"(h*e?%*~to~row~6G
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*+Rk_\"-%'MATRIXG6#7
(7'!#;!\"*!#]!#A\"#X7'\"\"!#\"$@\"\"#;#\"%\")=\"\")#\"%(e\"F8#!%<JF57'
F2F2#\"&x9\"\"#6#\"&.!*)F4#!')y7\"F47'F2F2F2#\"(Az6%\"'Zi7#!(y8K#FH7'F
2F2F2F2#\")J>D?\"(h*e?7'F2F2F2F2#!)od\\GFN%'MatrixG" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#%3Searching~column~5G" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6%%3Added~row~5~times~G#\"(C32%\"(LJ*G%*~to~row~6G" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*+Rk_\"-%'MATRIXG6#7(7'!#;!\"*!#]!#A
\"#X7'\"\"!#\"$@\"\"#;#\"%\")=\"\")#\"%(e\"F8#!%<JF57'F2F2#\"&x9\"\"#6
#\"&.!*)F4#!')y7\"F47'F2F2F2#\"(Az6%\"'Zi7#!(y8K#FH7'F2F2F2F2#\")J>D?
\"(h*e?7'F2F2F2F2F2%'MatrixG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTA
BLEG6%\"*+Rk_\"-%'MATRIXG6#7(7'!#;!\"*!#]!#A\"#X7'\"\"!#\"$@\"\"#;#\"%
\")=\"\")#\"%(e\"F8#!%<JF57'F2F2#\"&x9\"\"#6#\"&.!*)F4#!')y7\"F47'F2F2
F2#\"(Az6%\"'Zi7#!(y8K#FH7'F2F2F2F2#\")J>D?\"(h*e?7'F2F2F2F2F2%'Matrix
G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Transpose(%);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*?Wk_\"-%'MATRIXG6#7'7(!
#;\"\"!F-F-F-F-7(!\"*#\"$@\"\"#;F-F-F-F-7(!#]#\"%\")=\"\")#\"&x9\"\"#6
F-F-F-7(!#A#\"%(e\"F7#\"&.!*)F1#\"(Az6%\"'Zi7F-F-7(\"#X#!%<JF2#!')y7\"
F1#!(y8K#FC#\")J>D?\"(h*e?F-%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "4 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 
1 }{PAGENUMBERS 0 1 2 33 1 1 }