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{SECT 0 {EXCHG {PARA 200 "" 0 "" {TEXT 202 30 "Matrices and matrix ope
rations" }{TEXT 203 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 
20 "with(LinearAlgebra);" }{MPLTEXT 1 205 0 "" }}}{EXCHG {PARA 202 "" 
0 "" {TEXT 203 41 "Here are several ways to define matrices:" }}}
{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 205 4 "A1:=" }{MPLTEXT 1 204 42 
"Matrix([[2,1,0,3],[-1,0,2,4],[4,-2,7,0]]);" }{MPLTEXT 1 205 0 "" }}}
{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 205 11 "A2:=Array([" }{MPLTEXT 
1 204 34 "[2,1,0,3],[-1,0,2,4],[4,-2,7,0]]);" }{MPLTEXT 1 205 0 "" }}}
{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 205 4 "A3:=" }{MPLTEXT 1 204 36 
"<<2,-1,4>|<1,0,-2>|<0,2,7>|<3,4,0>>;" }{MPLTEXT 1 205 0 "" }}}{EXCHG 
{PARA 201 "> " 0 "" {MPLTEXT 1 205 17 "A4:=Matrix(3,4,[[" }{MPLTEXT 1 
204 33 "2,1,0,3],[-1,0,2,4],[4,-2,7,0]]);" }{MPLTEXT 1 205 0 "" }}}
{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 205 22 "I3:=IdentityMatrix(3);" 
}}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 205 22 "I4:=IdentityMatrix(5)
;" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 205 16 "Multiply(I3,A4);" 
}}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 205 16 "Multiply(A4,I3);" }
{MPLTEXT 1 205 0 "" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 203 34 "Finding \+
the transpose of a matrix." }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 
205 19 "A3t:=Transpose(A3);" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 203 76 
"Let us multiply the matrix A3 with its transpose A3t, and also A3t wi
th A3. " }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 205 21 "B1:=Multiply
(A3,A3t);" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 205 20 "B2=Multipl
y(A3t,A3);" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 203 49 "As you can see t
he two products are not the same." }}}{EXCHG {PARA 201 "> " 0 "" 
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