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{SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT 256 20 "Brettscher Exercises" }
}{PARA 19 "" 0 "" {TEXT 258 25 "BrettscherExercisesR7.mws" }}{PARA 
259 "" 0 "" {TEXT 257 14 "Brian E. Blank" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 84 "Click on a [+]  sign to \+
expand a section. Click on a [-] sign to collapse a section." }}}
{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 " 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 "   " }{HYPERLNK 17 "addrow" 2 "linalg[a
ddrow]" "" }{TEXT -1 3 ",  " }}{PARA 15 "" 0 "" {TEXT -1 3 "   " }
{HYPERLNK 17 "augment" 2 "linalg[augment]" "" }{TEXT -1 1 "," }}{PARA 
15 "" 0 "" {TEXT -1 3 "   " }{HYPERLNK 17 "evalm" 2 "evalm" "" }{TEXT 
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2 "linalg" "" }{TEXT -1 2 ", " }}{PARA 15 "" 0 "" {TEXT -1 3 "   " }
{HYPERLNK 17 "linsolve" 2 "linsolve" "" }{TEXT -1 2 ", " }}{PARA 15 "
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2 "mulrow" "" }{TEXT -1 3 ",  " }}{PARA 15 "" 0 "" {TEXT -1 3 "   " }
{HYPERLNK 17 "rref" 2 "linalg[rref]" "" }{TEXT -1 3 ",  " }}{PARA 15 "
" 0 "" {TEXT -1 3 "   " }{HYPERLNK 17 "swaprow" 2 "linalg[swaprow]" "
" }{TEXT -1 2 ", " }}{PARA 15 "" 0 "" {TEXT -1 3 "   " }{HYPERLNK 17 "
vector" 2 "vector" "" }{TEXT -1 1 "," }}{PARA 15 "" 0 "" {TEXT -1 3 " \+
  " }{HYPERLNK 17 "with" 2 "with" "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 
" Description" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 70 "  This worksheet consists of worked exercises from Otto B
rettscher's  " }{TEXT 259 32 "Linear Algebra with Applications" }
{TEXT -1 18 ",  second edition." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 8 " 1.1 #26" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "Consider the linear system" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 "         \+
    " }{XPPEDIT 19 1 "x+y-z=2" "6#/,(%\"xG\"\"\"%\"yGF&%\"zG!\"\"\"\"#
" }}{PARA 0 "" 0 "" {TEXT -1 13 "             " }{XPPEDIT 19 1 "x+2*y+
z=3" "6#/,(%\"xG\"\"\"*&\"\"#F&%\"yGF&F&%\"zGF&\"\"$" }}{PARA 0 "" 0 "
" {TEXT -1 13 "             " }{XPPEDIT 19 1 "x+y+(k^2-5)*z=k" "6#/,(%
\"xG\"\"\"%\"yGF&*&,&*$%\"kG\"\"#F&\"\"&!\"\"F&%\"zGF&F&F+" }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 12 "For which   " }{XPPEDIT 19 1 "k" "6#%\"kG" }{TEXT -1 
89 "   does the system have a unique solution?    Infinitely many solu
tions?    No solutions?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 260 9 "Solution:" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "wi
th(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "M := k -> ma
trix(3,4,[1,1,-1,2,1,2,1,3,1,1,k^2-5,k]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"MGf*6#%\"kG6\"6$%)operatorG%&arrowGF(-%'matrixG6%\"
\"$\"\"%7.\"\"\"F2!\"\"\"\"#F2F4F2F/F2F2,&*$9$F4F2!\"&F2F7F(F(6\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "M1 := delcols(M(k), 4..4);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M1G-%'MATRIXG6#7%7%\"\"\"F*!\"\"7
%F*\"\"#F*7%F*F*,&*$%\"kGF-F*!\"&F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 75 "linsolve(M1, col(M(k),4));  # As long as k <> -2 ther
e is a unique solution" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'VECTORG6#
7%*&,&%\"kG\"\"\"\"\"&F*F*,&F)F*\"\"#F*!\"\"*&F)F*F,F.*$F,F." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "rref(M(k));   # Another way \+
of seeing the same thing." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIX
G6#7%7&\"\"\"\"\"!F)*&,&%\"kGF(\"\"&F(F(,&F,F(\"\"#F(!\"\"7&F)F(F)*&F,
F(F.F07&F)F)F(*$F.F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "rre
f(M(-2));  # The system is inconsistent (no solutions) when  k = -2" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7%7&\"\"\"\"\"!!\"$F)7&F)
F(\"\"#F)7&F)F)F)F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "           " }}{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 33 " Copyright and
 Author Information" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 0 
"" {TEXT -1 60 "  BrettscherExercisesR7.mws     A Maple Release 7 work
sheet." }}{PARA 261 "" 0 "" {TEXT -1 26 "  Author:  Brian E. Blank " }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 262 "" 0 "" {TEXT -1 23 "  Date
:  29 August 2001" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 53 "  This document may not be distributed by any medium," }}
{PARA 0 "" 0 "" {TEXT -1 57 "  including print, disk, and electronic t
ransfer, without" }}{PARA 0 "" 0 "" {TEXT -1 41 "  prior written permi
ssion of the author." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 263 "" 
0 "" {TEXT -1 51 "  For more information,  please contact the author:
" }}{PARA 264 "" 0 "" {TEXT -1 4 "    " }}{PARA 264 "" 0 "" {TEXT -1 
34 "       Department of Mathematics, " }}{PARA 0 "" 0 "" {TEXT -1 41 
"       Washington University in St. Louis" }}{PARA 0 "" 0 "" {TEXT 
-1 28 "       St. Louis, MO   63130" }}{PARA 0 "" 0 "" {TEXT -1 3 "   \+
" }}{PARA 0 "" 0 "" {TEXT -1 35 "       Telephone:    (314) 935-6763" 
}}{PARA 265 "" 0 "" {TEXT -1 46 "               e-mail:    brian@math.
wustl.edu" }}{PARA 266 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 58 "  Copyright:  \251 2001 Brian E. Blank,  All Rights Reserved." 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK "0 1 0" 21 }{VIEWOPTS 1 1 0 
3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }