{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 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 "Headi ng 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Mat2705-01/04 05S Quiz 5 M aple check" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg): " }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 18 "1. det and lin dep" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "augment([3,-1,2],[2,-3,5],[3 ,-1,2]-[2,-3,5]);\ndet(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "Det erminant is zero, so vectors are not linearly independent." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "augment([1,-1,2],[3,0,1],[1,-2,2]); \ndet(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "Determinant is not z ero, so vectors are linearly independent." }}}}{SECT 0 {PARA 3 "" 0 " " {TEXT -1 55 "2. express given vector as lin comb of a set of vectors " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "A:=augment([1,-2,2],[3,0 ,1],[1,-1,2]);\nw:=[2,-7,9];\naugment(A,w);\nrref(%);\n[x1,x2,x3]=back sub(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "[2,-7,9]=2*col(A ,1)-col(A,2)+3*col(A,3);\nevalm(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 51 "3. solve a \+ lin hom sys to find linear relationships" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "a) matrix form of linear system" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "A:=matrix([[1,3,3,3],[2,7,5,-1],[2,7,4,-4]]);\nb :=augment([0,0,0]);\nx:=augment([x1,x2,x3]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "evalm(A)&*evalm(x)=evalm(b);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "b) solution" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "augment(A,b);\nrref(%);\n[x1,x2,x3]=backsub(%);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "c) factored solution" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "[x1, x2, x3] = _t[1]*[-6, 4, -3, 1] ;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "d) independent linear relati onships among columns of A:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "-6*col(A,1)+4*col(A,2)-3*col(A,3)+col(A,4)=[0,0,0];\nevalm(%);" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "0 0 0" 36 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }