{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {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 " " -1 256 "" 1 24 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 128 0 1 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 18 0 0 0 0 0 1 0 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 "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 "Tit le" 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 "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 "R3 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 "" 3 259 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 "" 3 260 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 "" 0 261 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 } {PSTYLE "" 0 268 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 "" 0 269 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 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 259 20 "Student Name and ID:" }} {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 12 "Introd uction" }}{PARA 0 "" 0 "" {TEXT -1 9 "In this " }{TEXT 257 5 "MAPLE" }{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 1 {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 " " } {HYPERLNK 17 "addrow" 2 "linalg[addrow]" "" }{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 "ditto" 2 "ditto" "" }{TEXT -1 1 "," }}{PARA 15 "" 0 "" {TEXT -1 3 " " }{HYPERLNK 17 "dotprod" 2 "dotprod" "" }{TEXT -1 2 ", " }}{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 "rank" 2 "linalg[rank]" "" }{TEXT -1 4 ", " }}{PARA 15 "" 0 "" {TEXT -1 3 " " }{HYPERLNK 17 "restart" 2 "restart" "" } {TEXT -1 1 "," }}{PARA 15 "" 0 "" {TEXT -1 3 " " }{HYPERLNK 17 "rref " 2 "linalg[rref]" "" }{TEXT -1 3 ", " }}{PARA 15 "" 0 "" {TEXT -1 3 " " }{HYPERLNK 17 "scalarmul" 2 "scalarmul" "" }{TEXT -1 1 "," }} {PARA 15 "" 0 "" {TEXT -1 3 " " }{HYPERLNK 17 "swaprow" 2 "linalg[sw aprow]" "" }{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 2 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 "Exercise 1 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "Background worksheet: " }{HYPERLNK 17 "eleme 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([[1, 0, 2, 1], [1, 0, 1, 0], [2, 3, 0, -4], [2, 8, -1, -8]])" "-%'MATRIXG6#7&7&\"\" \"\"\"!\"\"#F'7&F'F(F'F(7&F)\"\"$F(,$\"\"%!\"\"7&F)\"\"),$F'F/,$F1F/" }{TEXT -1 116 " by augmenting it with the identity matrix and obta ining the reduced row echelon form of the augmented matrix. " }} {PARA 0 "" 0 "" {TEXT -1 11 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {SECT 1 {PARA 259 "" 0 "" {TEXT -1 13 "Exercise 2 " }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "Background worksheet: \+ " }{HYPERLNK 17 "elementaryMatricesR4.mws" 1 "elementaryMatricesR4 .mws" "" }{TEXT -1 3 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 37 "Calculate the inverse matrix of " }{XPPEDIT 19 1 "MATRIX([[3, 1, 4], [1, 2, 0], [0, -1, 1]])" "-%'MATRIXG6#7%7%\" \"$\"\"\"\"\"%7%F(\"\"#\"\"!7%F,,$F(!\"\"F(" }{TEXT -1 56 " by wri ting it as a product of elementary matrices. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 260 "" 0 "" {TEXT -1 11 "Exercise 3 " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "Backgroun d worksheet: " }{HYPERLNK 17 "elementaryMatricesR4.mws" 1 "elemen taryMatricesR4.mws" "" }{TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 34 "Find the LU Decomposition of " } {XPPEDIT 19 1 "MATRIX([[1, 2, 3, 4], [0, 1, 3, 1], [1, 2, 2, 2], [0, 1 , 4, 2]])" "-%'MATRIXG6#7&7&\"\"\"\"\"#\"\"$\"\"%7&\"\"!F'F)F'7&F'F(F( F(7&F,F'F*F(" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Exercise 4" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "Background worksheet: \+ " }{HYPERLNK 17 "elementaryMatricesR4.mws" 1 "elementaryMatricesR4.mws " "" }{TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 6 "Let " }{XPPEDIT 19 1 " A =MATRIX([[1, 2, 3, 4], [0, 1, 3, 1], [1, 2, 2, 2], [0, 1, 4, 2]])" " /%\"AG-%'MATRIXG6#7&7&\"\"\"\"\"#\"\"$\"\"%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 d ecomposition of the given matrix (calculated in Exercise 3) to solve t he system\n\n " }{XPPEDIT 19 1 "MATRIX([[1, 2, 3 , 4], [0, 1, 3, 1], [1, 2, 2, 2], [0, 1, 4, 2]])*MATRIX( [ [x[1]],[x[2 ]],[x[3]],[x[4]]] )=MATRIX( [ [0],[-1],[0],[-2] ] )" "/*&-%'MATRIXG 6#7&7&\"\"\"\"\"#\"\"$\"\"%7&\"\"!F)F+F)7&F)F*F*F*7&F.F)F,F*F)-F%6#7&7 #&%\"xG6#F)7#&F66#F*7#&F66#F+7#&F66#F,F)-F%6#7&7#F.7#,$F)!\"\"7#F.7#,$ F*FG" }{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 1 {PARA 3 "" 0 "" {TEXT -1 32 " Copyright and Author Information" }}{EXCHG {PARA 261 "" 0 "" {TEXT -1 50 "M309S04hw2R4.mws A MapleV Release 4 worksheet." }}{PARA 262 " " 0 "" {TEXT -1 0 "" }}{PARA 263 "" 0 "" {TEXT -1 43 "Author: Brian E . Blank (24 February 2004)" }}{PARA 264 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 51 "This document may not be distributed by a ny medium," }}{PARA 0 "" 0 "" {TEXT -1 55 "including print, disk, and \+ electronic transfer, without" }}{PARA 0 "" 0 "" {TEXT -1 39 "prior wri tten permission of the author." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 265 "" 0 "" {TEXT -1 49 "For more information, please contact t he author:" }}{PARA 266 "" 0 "" {TEXT -1 4 " " }}{PARA 266 "" 0 "" {TEXT -1 32 " Department of Mathematics, " }}{PARA 0 "" 0 "" {TEXT -1 39 " Washington University in St. Louis" }}{PARA 0 "" 0 " " {TEXT -1 26 " St. Louis, MO 63130" }}{PARA 0 "" 0 "" {TEXT -1 3 " " }}{PARA 0 "" 0 "" {TEXT -1 33 " Telephone: (314) 935-67 63" }}{PARA 267 "" 0 "" {TEXT -1 44 " e-mail: brian@mat h.wustl.edu" }}{PARA 268 "" 0 "" {TEXT -1 0 "" }}{PARA 269 "" 0 "" {TEXT -1 56 "Copyright: \251 2004 Brian E. Blank, All Rights Reserve d." }}}}}{MARK "4" 0 }{VIEWOPTS 1 1 0 3 4 1802 }