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2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic" -1 3 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }} {SECT 0 {EXCHG {PARA 203 "" 0 "" {TEXT 208 30 "Matrices and matrix op erations" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 209 20 "with(Linear Algebra);" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 201 41 "Here are several \+ ways to define matrices:" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 203 4 "A1:=" }{MPLTEXT 1 209 42 "Matrix([[2,1,0,3],[-1,0,2,4],[4,-2,7, 0]]);" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 203 11 "A2:=Array([" } {MPLTEXT 1 209 34 "[2,1,0,3],[-1,0,2,4],[4,-2,7,0]]);" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 203 4 "A3:=" }{MPLTEXT 1 209 36 "<<2,-1 ,4>|<1,0,-2>|<0,2,7>|<3,4,0>>;" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 203 17 "A4:=Matrix(3,4,[[" }{MPLTEXT 1 209 33 "2,1,0,3],[-1,0,2,4], [4,-2,7,0]]);" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 203 22 "I3:=Id entityMatrix(3);" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 203 22 "I4: =IdentityMatrix(5);" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 203 16 " Multiply(I3,A4);" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 203 16 "Mul tiply(A4,I3);" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 201 34 "Finding the t ranspose of a matrix." }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 203 19 "A3t:=Transpose(A3);" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 201 76 "Let us multiply the matrix A3 with its transpose A3t, and also A3t with A 3. " }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 203 21 "B1:=Multiply(A3, A3t);" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 203 20 "B2=Multiply(A3 t,A3);" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 201 49 "As you can see the t wo products are not the same." }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 203 0 "" }}}{PARA 208 "" 0 "" {TEXT 210 0 "" }}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }