{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Tim es" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 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 0 "" 0 "" {TEXT -1 79 "Mat2705 03S Quiz 5 Print N ame (Last,First): ___________________________________" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "A:=matrix([[5,6,1,2,5,6,1,0],[3,4,3,4,7,8,0,1 ]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7$7*\"\"&\" \"'\"\"\"\"\"#F*F+F,\"\"!7*\"\"$\"\"%F0F1\"\"(\"\")F.F," }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 3 "a) " }{TEXT 258 100 "Give the sequence o f row operations (in order) needed to row reduce this matrix using the notation: " }{TEXT -1 6 "mulrow" }{TEXT 262 15 "(%,row#,coef), " } {TEXT -1 6 "addrow" }{TEXT 263 23 "(%,row#, torow#,coef), " }{TEXT -1 7 "swaprow" }{TEXT 264 13 "(%,row#,row#)" }}{PARA 0 "" 0 "" {TEXT -1 19 "and give the final " }{TEXT 257 4 "rref" }{TEXT -1 16 " reduced ma trix." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 2 "b)" }{TEXT -1 99 " Let C be the 2x4 matrix formed by deleting the last 4 columns from A and l et B be the 2x2 matrix:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 " B:=matrix([[4,-6],[-3,5]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG- %'matrixG6#7$7$\"\"%!\"'7$!\"$\"\"&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Evaluate the matrix product BC by hand." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 2 "c)" }{TEXT -1 211 " Based on your row reduction work so far and not by doing any further work, solve the following system \+ associated with the first 3 columns of A and explain how you obtained \+ your solution from your previous work:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " sys:=\{5*x+6*y=1,3*x+4*y=3\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$sysG<$/,&*&\"\"&\"\"\"%\"xGF*F**&\"\"'F*%\"yGF*F*F*/ ,&*&\"\"$F*F+F*F**&\"\"%F*F.F*F*F2" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 2 "d)" }{TEXT -1 59 " Write out the system of 2 linear equations i n 4 variables " }{XPPEDIT 18 0 "x1,x2,x3,x4;" "6&%#x1G%#x2G%#x3G%#x4G " }{TEXT -1 27 " which has the matrix form " }{XPPEDIT 18 0 "C*X = 0; " "6#/*&%\"CG\"\"\"%\"XGF&\"\"!" }{TEXT -1 247 ", where the 0 is the 2 x1 zero matrix. Again from your previous row reduction result, write o ut the equivalent linear system after the row reduction and solve it f or X, writing the result in column matrix form, and then pulling apart the solution: " }{XPPEDIT 18 0 "X = t[1]*C1+t[2]*C2;" "6#/%\"XG,&*&&% \"tG6#\"\"\"F*%#C1GF*F**&&F(6#\"\"#F*%#C2GF*F*" }{TEXT -1 90 " + ... b y expressing it in terms of the column matrices of coefficients of the parameters." }}}}{MARK "3 0 7" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }