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Click on a [-] sign to collapse a sec tion. To do these exercises you 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 the 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 0 {PARA 3 "" 0 "" {TEXT -1 12 "Introduction" }}{PARA 0 "" 0 "" {TEXT -1 9 "In \+ this " }{TEXT 257 5 "MAPLE" }{TEXT -1 3 " " }{HYPERLNK 17 "workshee t" 2 "worksheet" "" }{TEXT -1 125 ", you will be asked to to perform calculations pertaining to 1) diagonalization, and (2) orthonormaliz ation. You may use " }{TEXT 266 5 "MAPLE" }{TEXT -1 57 " to perform \+ the calculations or you may do them by hand." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 7 "Reports" }}{PARA 0 "" 0 "" {TEXT -1 30 "Reports that yo u prepare with " }{TEXT 267 5 "MAPLE" }{TEXT -1 112 " should be prep ared with the same care that you would devote to laboratory reports in biology and chemistry. " }{TEXT 269 46 "A report should not be a dia ry 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 need ed for the report." }{TEXT -1 25 " All lines of the form " }{TEXT 259 6 "?topic" }{TEXT -1 82 " (that arise from help queries) should b e erased. All errors should be erased. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "When you are printing a " }{TEXT 272 5 "MAPLE" }{TEXT -1 165 " report, think about the toner and paper resources that you are using. All commands must be terminated - eithe r with the standard terminator, the semicolon, or the " }{TEXT 276 17 "silent terminator" }{TEXT -1 57 ", the colon. When you assign a varia ble, for example \n \"" }{TEXT 277 7 "x := 5;" }{TEXT -1 30 " \", th ere 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 si mply wastes paper and ink. Choose the silent terminator \"" }{TEXT 261 7 "x := 5:" }{TEXT -1 70 " \" instead. 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 fa miliar with what " }{TEXT 275 5 "MAPLE" }{TEXT -1 125 " makes availab le. However, these commands should not be part of a lab report. Reload the package with the silent terminator. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 79 "Much of the text in this worksheet should be deleted. For example, delete the " }{TEXT 263 12 "Introduc tion" }{TEXT -1 5 " and " }{TEXT 264 8 "Keywords" }{TEXT -1 34 " secti ons. Delete this section on " }{TEXT 265 7 "Reports" }{TEXT -1 1 "." } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 235 "Remembe r that your worksheet should execute in the order that it has been wri tten. In particular, remember that the ditto refers to the result of \+ the last executed command - not the result of the command that physica lly precedes it. " }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 8 "Keywords" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 " Clickin g 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 "ad drow" 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 "ditt o" 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 "lina lg" "" }{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 0 {PARA 3 "" 0 "" {TEXT -1 12 "Exercise 1 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 9 "Let " } {XPPEDIT 19 1 "A=MATRIX([[14, 24, 12, -24], [6, 14, 6, -12], [3, 6, 5, -6], [15, 30, 15, -28]])" "/%\"AG-%'MATRIXG6#7&7&\"#9\"#C\"#7,$F*!\" \"7&\"\"'F)F/,$F+F-7&\"\"$F/\"\"&,$F/F-7&\"#:\"#IF6,$\"#GF-" }{TEXT -1 3 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 17 "Find a matrix " }{XPPEDIT 19 1 "P" "I\"PG6\"" }{TEXT -1 15 " such that " }{XPPEDIT 19 1 "P *A * P ^(-1)" "*(%\"PG\"\"\"%\"AGF$)F#,$F$!\"\"F$" }{TEXT -1 18 " is diag onal. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 259 "" 0 "" {TEXT -1 13 "Exercise 2 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 7 "Let " }{XPPEDIT 19 1 "v[1]=MATRIX([[ 1], [ 0], [2], [-1]])" "/&%\"vG6#\"\"\"-%'MATRIXG6#7&7 #F&7#\"\"!7#\"\"#7#,$F&!\"\"" }{TEXT -1 6 ", " }{XPPEDIT 19 1 "v[2 ]=MATRIX([[ 1], [ 0], [0], [-1]])" "/&%\"vG6#\"\"#-%'MATRIXG6#7&7#\"\" \"7#\"\"!7#F.7#,$F,!\"\"" }{TEXT -1 5 ", " }{XPPEDIT 19 1 "v[3]=MAT RIX([[ 0], [ 1], [0], [2]])" "/&%\"vG6#\"\"$-%'MATRIXG6#7&7#\"\"!7#\" \"\"7#F,7#\"\"#" }{TEXT -1 3 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 80 "Apply the Gram-Schmidt process to find an orthonormal basis of the subspace of \+ " }{XPPEDIT 19 1 "R^4" "*$%\"RG\"\"%" }{TEXT -1 41 " that is spanned by these three vectors." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 11 "Exercise \+ 3 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 30 "Fin d an orthonormal basis of " }{XPPEDIT 19 1 "R^4" "*$%\"RG\"\"%" } {TEXT -1 75 " that includes the three vectors that you found in the p receding exercise." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 260 "" 0 "" {TEXT -1 11 "Exercise 4 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 7 "Let " }{XPPEDIT 19 1 "S=MATRIX([[-2/3 , 2/3, -2/3], [2/3, 7/3, 2/3], [-2/3, 2/3, 7/3]])" "/%\"SG-%'MATRIXG6# 7%7%,$*&\"\"#\"\"\"\"\"$!\"\"F.*&F+F,F-F.,$*&F+F,F-F.F.7%*&F+F,F-F.*& \"\"(F,F-F.*&F+F,F-F.7%,$*&F+F,F-F.F.*&F+F,F-F.*&F5F,F-F." }{TEXT -1 2 ".\n" }}{PARA 0 "" 0 "" {TEXT -1 10 "Find an " }{TEXT 291 10 "orth ogonal" }{TEXT -1 12 " matrix " }{XPPEDIT 19 1 "P" "I\"PG6\"" } {TEXT -1 16 " such that " }{XPPEDIT 19 1 "P^t*S*P" "*()%\"PG%\"tG \"\"\"%\"SGF&F$F&" }{TEXT -1 17 " is diagonal. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 32 "Copyright and Author Information" }}{EXCHG {PARA 261 " " 0 "" {TEXT -1 50 "M309F03hw6R4.mws A MapleV Release 4 worksheet. " }}{PARA 262 "" 0 "" {TEXT -1 0 "" }}{PARA 263 "" 0 "" {TEXT -1 42 "A uthor: Brian E. Blank (2 December 2003)" }}{PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "This document may not be distri buted by any medium," }}{PARA 0 "" 0 "" {TEXT -1 55 "including print, \+ disk, and electronic transfer, without" }}{PARA 0 "" 0 "" {TEXT -1 39 "prior written permission of the author." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 265 "" 0 "" {TEXT -1 49 "For more information, please co ntact 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.wustl.edu" }}{PARA 268 "" 0 "" {TEXT -1 0 "" }}{PARA 269 "" 0 "" {TEXT -1 56 "Copyright: \251 2003 Brian E. Blank, All Rights Reserve d." }}}}}{MARK "5 3 2" 0 }{VIEWOPTS 1 1 0 3 4 1802 }