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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:" }} {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 28 ", you will be asked to use " }{TEXT 266 5 "MAPLE" }{TEXT -1 76 " to perform calculations with inverses of matrices and elementary matrices." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 7 "Reports" }}{PARA 0 "" 0 "" {TEXT -1 30 "Reports that you prepare with " }{TEXT 267 5 "MAP LE" }{TEXT -1 112 " should be prepared with the same care that you w ould devote to laboratory reports in biology and chemistry. " }{TEXT 269 46 "A report should not be a diary or history of a" }{TEXT -1 1 " \+ " }{TEXT 268 6 " MAPLE" }{TEXT -1 2 " " }{TEXT 270 1 " " }{TEXT 271 51 "session. Delete what is not needed for the report." }{TEXT -1 25 " All lines of the form " }{TEXT 259 6 "?topic" }{TEXT -1 82 " (tha t arise from help queries) should be erased. All errors should be era sed. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "When you are printing a " }{TEXT 272 5 "MAPLE" }{TEXT -1 165 " repor t, think about the toner and paper resources that you are using. All c ommands must be terminated - either with the standard terminator, the \+ semicolon, or the " }{TEXT 276 17 "silent terminator" }{TEXT -1 57 ", \+ the colon. When you assign a variable, for example \n \"" }{TEXT 277 7 "x := 5;" }{TEXT -1 30 " \", there is no need to have " }{TEXT 273 5 "MAPLE" }{TEXT -1 12 " echo back " }{TEXT 260 6 "x := 5" }{TEXT -1 89 ". When this is printed, it simply wastes paper and ink. Choose t he silent terminator \"" }{TEXT 261 7 "x := 5:" }{TEXT -1 70 " \" in stead. When you load a package (without the silent terminator)," } {TEXT 262 1 " " }{TEXT -1 2 " " }{TEXT 274 5 "MAPLE" }{TEXT -1 123 " \+ will list the commands that become available with the package. This is fine - it will help you become familiar with what " }{TEXT 275 5 "MA PLE" }{TEXT -1 125 " makes available. However, these commands should n ot be part of a lab report. Reload the package with the silent termina tor. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 79 " Much of the text in this worksheet should be deleted. For example, de lete the " }{TEXT 263 12 "Introduction" }{TEXT -1 5 " and " }{TEXT 264 8 "Keywords" }{TEXT -1 34 " sections. Delete this section on " } {TEXT 265 7 "Reports" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 235 "Remember that your worksheet should ex ecute in the order that it has been written. In particular, remember \+ that the ditto refers to the result of the last executed command - not the result of the command that physically precedes it. " }}}{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 br ing 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 "au gment" 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 "mat rix" 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 "r estart" 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 "scalarm ul" "" }{TEXT -1 1 "," }}{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 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 "elementaryMatricesR4.mws" 1 "elementaryMatricesR4.mws " "" }{TEXT -1 4 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 36 "Calculate 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 65 " by augmenting it with the identity \+ matrix and row reducing ." }}{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 "Exer cise 2 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "Background worksheet: " }{HYPERLNK 17 "elementaryMatricesR4.m ws" 1 "elementaryMatricesR4.mws" "" }{TEXT -1 3 " " }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 34 "Calculate the inverse m atrix of " }{XPPEDIT 19 1 "MATRIX([[2, 0, 3], [1, 2, 0], [1, 1, 1]]) " "-%'MATRIXG6#7%7%\"\"#\"\"!\"\"$7%\"\"\"F'F(7%F+F+F+" }{TEXT -1 54 " by writing it as a product of elementary matrices. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 260 "" 0 "" {TEXT -1 11 "Exercise 3 " } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "Backgrou nd worksheet: " }{HYPERLNK 17 "elementaryMatricesR4.mws" 1 "eleme ntaryMatricesR4.mws" "" }{TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 31 "Find the LU Decomposition of " } {XPPEDIT 19 1 "MATRIX([[1, 2, 3, 4], [0, 1, 1, 1], [1, 1, 1, 0], [0, 1 , 2, 3]])" "-%'MATRIXG6#7&7&\"\"\"\"\"#\"\"$\"\"%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 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, 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 -1 154 "\nUse the LU d ecomposition of the given matrix (calculated in Exercise 3) to solve t he system Ax = s where s is the column vector with entries 2, 3, -3,8 ." }}{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 49 "309F01hw2R4.mws A MapleV Release 4 worksheet." }}{PARA 262 "" 0 "" {TEXT -1 0 "" }}{PARA 263 "" 0 "" {TEXT -1 44 "Author: Brian E. \+ Blank (20 September 2001)" }}{PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "This document may not be distributed by any med ium," }}{PARA 0 "" 0 "" {TEXT -1 55 "including print, disk, and electr onic transfer, without" }}{PARA 0 "" 0 "" {TEXT -1 39 "prior written p ermission of the author." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 265 "" 0 "" {TEXT -1 49 "For more 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 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) 935-6763" }} {PARA 267 "" 0 "" {TEXT -1 44 " e-mail: brian@math.wust l.edu" }}{PARA 268 "" 0 "" {TEXT -1 0 "" }}{PARA 269 "" 0 "" {TEXT -1 56 "Copyright: \251 2001 Brian E. Blank, All Rights Reserved." }}}}} {MARK "7" 0 }{VIEWOPTS 1 1 0 3 4 1802 }