{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 0 0 1 0 0 0 0 0 0 } {CSTYLE "2D Input" 2 19 "" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "2 D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 256 " " 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 338 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 339 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 0 0 0 0 0 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Ou tput" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Bullet Item" 0 15 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 3 3 0 0 0 0 0 0 15 2 } {PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R 3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 0 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 18 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 19 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 262 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 263 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 264 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 } 0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 265 1 {CSTYLE "" -1 -1 " " 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 266 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 } 0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 267 1 {CSTYLE "" -1 -1 " " 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT 256 20 "Brettscher Exercises" } }{PARA 19 "" 0 "" {TEXT 258 25 "BrettscherExercisesR4.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 -1 2 ", " }}{PARA 15 "" 0 "" {TEXT -1 3 " " }{HYPERLNK 17 "linalg" 2 "linalg" "" }{TEXT -1 2 ", " }}{PARA 15 "" 0 "" {TEXT -1 3 " " } {HYPERLNK 17 "linsolve" 2 "linsolve" "" }{TEXT -1 2 ", " }}{PARA 15 " " 0 "" {TEXT -1 3 " " }{HYPERLNK 17 "matrix" 2 "matrix" "" }{TEXT -1 2 ", " }}{PARA 15 "" 0 "" {TEXT -1 3 " " }{HYPERLNK 17 "mulrow" 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 338 32 "Linear Algebra with Applications" } {TEXT -1 18 ", second edition." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {SECT 1 {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" "/,(%\"xG\"\"\"%\"yGF%%\"zG!\"\"\"\"#" }}{PARA 0 "" 0 "" {TEXT -1 13 " " }{XPPEDIT 19 1 "x+2*y+z= 3" "/,(%\"xG\"\"\"*&\"\"#F%%\"yGF%F%%\"zGF%\"\"$" }}{PARA 0 "" 0 "" {TEXT -1 13 " " }{XPPEDIT 19 1 "x+y+(k^2-5)*z=k" "/,(%\"xG \"\"\"%\"yGF%*&,&*$%\"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" "I\"kG6\"" }{TEXT -1 89 " does the system have a unique solution? Infinitely many solutio ns? No solutions?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 339 9 "Solution:" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with( linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "M := k -> matri x(3,4,[1,1,-1,2,1,2,1,3,1,1,k^2-5,k]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG:6#%\"kG6\"6$%)operatorG%&arrowGF(-%'matrixG6%\"\"$\"\"%7. \"\"\"F2!\"\"\"\"#F2F4F2F/F2F2,&*$9$F4F2!\"&F2F7F(F(" }}}{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*,&*$%\"kGF-F*!\"&F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 " linsolve(M1, col(M(k),4)); # As long as k <> -2 there is a unique sol ution" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'VECTORG6#7%*&,&%\"kG\"\"\" \"\"&F*F*,&F)F*\"\"#F*!\"\"*&F)F*F,F.*$F,F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "rref(M(k)); # Another way of seeing the same thi ng." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7%7&\"\"\"\"\"!F)*& ,&%\"kGF(\"\"&F(F(,&F,F(\"\"#F(!\"\"7&F)F(F)*&F,F(F.F07&F)F)F(*$F.F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "rref(M(-2)); # The syste m is inconsistent (no solutions) when k = -2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7%7&\"\"\"\"\"!!\"$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 1 {PARA 3 "" 0 "" {TEXT -1 33 " Copyright and Author Informati on" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 0 "" {TEXT -1 61 " \+ BrettscherExercisesR4.mws A MapleV Release 4 worksheet." }}{PARA 262 "" 0 "" {TEXT -1 26 " Author: Brian E. Blank " }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 263 "" 0 "" {TEXT -1 23 " Date: 29 August 20 01" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 53 " T his document may not be distributed by any medium," }}{PARA 0 "" 0 "" {TEXT -1 57 " including print, disk, and electronic transfer, without " }}{PARA 0 "" 0 "" {TEXT -1 41 " prior written permission of the aut hor." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT -1 51 " For more information, please contact the author:" }}{PARA 265 "" 0 "" {TEXT -1 4 " " }}{PARA 265 "" 0 "" {TEXT -1 34 " Departm ent of Mathematics, " }}{PARA 0 "" 0 "" {TEXT -1 41 " Washington University in St. Louis" }}{PARA 0 "" 0 "" {TEXT -1 28 " St. Lo uis, MO 63130" }}{PARA 0 "" 0 "" {TEXT -1 3 " " }}{PARA 0 "" 0 "" {TEXT -1 35 " Telephone: (314) 935-6763" }}{PARA 266 "" 0 "" {TEXT -1 46 " e-mail: brian@math.wustl.edu" }}{PARA 267 "" 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 "5" 0 }{VIEWOPTS 1 1 0 3 4 1802 }