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0 0 -1 0 } {PSTYLE "" 0 306 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 307 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 308 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 309 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 0 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 257 20 "Systems of Equations" } }{PARA 258 "" 0 "" {TEXT 256 4 "HW 1" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 111 "Click on a [+] sign to expa nd a section. Click on a [-] sign to collapse a section. To do these e xercises in " }{TEXT 272 5 "Maple" }{TEXT -1 154 " you will have to i nsert execution groups. That can be done by clicking on the toolbar ic on 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 258 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 9 " Useful " }{TEXT 271 5 "Maple" }{TEXT -1 10 " Commands" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 60 " Clicking on any of these words will brin g 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 21 " Reference Worksheets" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "Background worksh eet: " }{HYPERLNK 17 "rowreductionR4.mws" 1 "rowreductionR4.mws" " " }{TEXT -1 4 " " }}{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 3 " " }} {PARA 0 "" 0 "" {TEXT -1 152 "Write down the augmented matrix of the f ollowing linear system of six equations in six unknowns. Then, using r ow operations, solve the following system:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 270 "" 0 "" {TEXT -1 5 " " }{TEXT 261 4 " " } {XPPEDIT 262 1 "u + v + 3*w - x + 3*y - z = 14" "/,.%\"uG\"\"\"%\"vGF% *&\"\"$F%%\"wGF%F%%\"xG!\"\"*&F(F%%\"yGF%F%%\"zGF+\"#9" }}{PARA 271 " " 0 "" {TEXT -1 2 " " }}{PARA 272 "" 0 "" {TEXT -1 8 " " } {XPPEDIT 19 1 "2*u + v + w + x + y + 3*z = 7" "/,.*&\"\"#\"\"\"%\"uGF& F&%\"vGF&%\"wGF&%\"xGF&%\"yGF&*&\"\"$F&%\"zGF&F&\"\"(" }}{PARA 273 "" 0 "" {TEXT -1 0 "" }}{PARA 274 "" 0 "" {TEXT -1 8 " " } {XPPEDIT 19 1 "w - x + y - z = 2" "/,*%\"wG\"\"\"%\"xG!\"\"%\"yGF%%\"z GF'\"\"#" }}{PARA 275 "" 0 "" {TEXT -1 1 " " }}{PARA 276 "" 0 "" {TEXT -1 8 " " }{XPPEDIT 19 1 "u+4*v - w + 2*x + y + z = 3" "/ ,.%\"uG\"\"\"*&\"\"%F%%\"vGF%F%%\"wG!\"\"*&\"\"#F%%\"xGF%F%%\"yGF%%\"z GF%\"\"$" }}{PARA 277 "" 0 "" {TEXT -1 0 "" }}{PARA 278 "" 0 "" {TEXT -1 8 " " }{XPPEDIT 19 1 "6*u+8*v + 2*z = 4" "/,(*&\"\"'\"\"\"% \"uGF&F&*&\"\")F&%\"vGF&F&*&\"\"#F&%\"zGF&F&\"\"%" }}{PARA 279 "" 0 " " {TEXT -1 0 "" }}{PARA 280 "" 0 "" {TEXT 259 8 " " }{XPPEDIT 260 1 "5*u -4*v + 3*w - 2*x + y = 22" "/,,*&\"\"&\"\"\"%\"uGF&F&*&\"\" %F&%\"vGF&!\"\"*&\"\"$F&%\"wGF&F&*&\"\"#F&%\"xGF&F+%\"yGF&\"#A" }} {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 0 "" }}{PARA 0 "" 0 "" {TEXT -1 152 "Write down the augmented matrix of the following linear system of six equations in six unknowns. Then, using row operations, solve the following system:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 281 "" 0 "" {TEXT -1 5 " " }{TEXT 265 4 " " } {XPPEDIT 266 1 "u + v + 3*w - x + 3*y - z = 14" "/,.%\"uG\"\"\"%\"vGF% *&\"\"$F%%\"wGF%F%%\"xG!\"\"*&F(F%%\"yGF%F%%\"zGF+\"#9" }}{PARA 282 " " 0 "" {TEXT -1 2 " " }}{PARA 283 "" 0 "" {TEXT -1 8 " " } {XPPEDIT 19 1 "2*u + v + w + x + y + 3*z = 7" "/,.*&\"\"#\"\"\"%\"uGF& F&%\"vGF&%\"wGF&%\"xGF&%\"yGF&*&\"\"$F&%\"zGF&F&\"\"(" }}{PARA 284 "" 0 "" {TEXT -1 0 "" }}{PARA 285 "" 0 "" {TEXT -1 8 " " } {XPPEDIT 19 1 "w - x + y - z = 2" "/,*%\"wG\"\"\"%\"xG!\"\"%\"yGF%%\"z GF'\"\"#" }}{PARA 286 "" 0 "" {TEXT -1 1 " " }}{PARA 287 "" 0 "" {TEXT -1 8 " " }{XPPEDIT 19 1 "u+4*v - w + 2*x + y + z = 3" "/ ,.%\"uG\"\"\"*&\"\"%F%%\"vGF%F%%\"wG!\"\"*&\"\"#F%%\"xGF%F%%\"yGF%%\"z GF%\"\"$" }}{PARA 288 "" 0 "" {TEXT -1 0 "" }}{PARA 289 "" 0 "" {TEXT -1 8 " " }{XPPEDIT 19 1 "4*u+9*v + 4*x+4*y + 4*z = 15" "/,,*&\" \"%\"\"\"%\"uGF&F&*&\"\"*F&%\"vGF&F&*&F%F&%\"xGF&F&*&F%F&%\"yGF&F&*&F% F&%\"zGF&F&\"#:" }}{PARA 290 "" 0 "" {TEXT -1 0 "" }}{PARA 291 "" 0 " " {TEXT 263 8 " " }{XPPEDIT 264 1 "u +2*v + 2*w + 2*x + 2*y = 2 3" "/,,%\"uG\"\"\"*&\"\"#F%%\"vGF%F%*&F'F%%\"wGF%F%*&F'F%%\"xGF%F%*&F' F%%\"yGF%F%\"#B" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {SECT 1 {PARA 260 "" 0 "" {TEXT -1 11 "Exercise 3 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 37 "Find the reduced row eche lon form of " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 292 "" 0 "" {TEXT -1 5 " " }{TEXT 269 4 " " }{XPPEDIT 270 1 "MATRIX([[0, 1, 2, -1, 4, 0, -1], [-3, 1, -7, -2, 19, -1, 3], [5, 4, 23, -1, -13, 0, \+ -1], [2, 9, 24, -6, 19, -2, 0], [1, 8, 19, -6, 22, -3, 1], [1, 3, 9, - 2, 5, -1, 0]])" "-%'MATRIXG6#7(7)\"\"!\"\"\"\"\"#,$F(!\"\"\"\"%F',$F(F +7),$\"\"$F+F(,$\"\"(F+,$F)F+\"#>,$F(F+F07)\"\"&F,\"#B,$F(F+,$\"#8F+F' ,$F(F+7)F)\"\"*\"#C,$\"\"'F+F4,$F)F+F'7)F(\"\")F4,$FAF+\"#A,$F0F+F(7)F (F0F>,$F)F+F7,$F(F+F'" }}{PARA 293 "" 0 "" {TEXT -1 2 " " }}{PARA 294 "" 0 "" {TEXT -1 3 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Exercise 4 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }} {PARA 0 "" 0 "" {TEXT -1 236 "Write down the augmented matrix of the f ollowing linear system of three equations in four unknowns. Using row \+ operations, find an equivalent system whose associated matrix is upper triangular. Then solve the system by back substitution:" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 303 "" 0 "" {TEXT -1 5 " " }{TEXT 273 4 " " }{XPPEDIT 274 1 "w + x + 3*y + z = 10" "/,*%\"wG\"\"\"%\" xGF%*&\"\"$F%%\"yGF%F%%\"zGF%\"#5" }}{PARA 304 "" 0 "" {TEXT -1 2 " \+ " }}{PARA 305 "" 0 "" {TEXT -1 8 " " }{XPPEDIT 19 1 "2*w + 2*x \+ + 2*y - z = 20" "/,**&\"\"#\"\"\"%\"wGF&F&*&F%F&%\"xGF&F&*&F%F&%\"yGF& F&%\"zG!\"\"\"#?" }}{PARA 306 "" 0 "" {TEXT -1 0 "" }}{PARA 307 "" 0 " " {TEXT -1 8 " " }{XPPEDIT 19 1 "w - x + y = 5" "/,(%\"wG\"\" \"%\"xG!\"\"%\"yGF%\"\"&" }}{PARA 308 "" 0 "" {TEXT -1 1 " " }}{PARA 309 "" 0 "" {TEXT -1 1 " " }}{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 "309S0 4hw1R4.mws A MapleV Release 4 worksheet." }}{PARA 262 "" 0 "" {TEXT -1 0 "" }}{PARA 263 "" 0 "" {TEXT -1 43 "Author: Brian E. Blank (12 February 2004)" }}{PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "This document may not be distributed by any medium, " }}{PARA 0 "" 0 "" {TEXT -1 55 "including print, disk, and electronic transfer, without" }}{PARA 0 "" 0 "" {TEXT -1 39 "prior written permi ssion 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.wustl.edu" }} {PARA 268 "" 0 "" {TEXT -1 0 "" }}{PARA 269 "" 0 "" {TEXT -1 56 "Copyr ight: \251 2004 Brian E. Blank, All Rights Reserved." }}}}}{MARK "5 \+ 0 0" 13 }{VIEWOPTS 1 1 0 3 4 1802 }