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{SECT 0 {PARA 260 "" 0 "" {TEXT -1 17 "Matrix Operations" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 190 "Maple's implement
ation of the basic matrix operations of addition, scalar multiplicatio
n, and matrix multiplication are illustrated below.  Things are mostly
 what you might expect; however, " }{TEXT 256 36 "there are some impor
tant differences" }{TEXT -1 159 ".  Be on the look out  for these as y
ou read through the discussion below.  First we need to load the linea
r algebra package, so execute the following command." }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT 258 17 "Defining a matrix" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "A := matrix([[1,2,3,4],[5,6,7,8],[9
,10,11,12]]);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "B := mat
rix(3,2,[1,2,3,4,5,6]);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
50 "C := matrix(3,3,(i,j)-> i*j);\nM := matrix(5,3,0);\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "I3 := diag(1$3);\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT 260 17 "Matrix operations" }}{PARA 0 "" 0 "" 
{TEXT -1 208 "     The following examples illustrate the matrix operat
ions we discussed in Sections 2.1-2.3 of our text.  Note that for addi
tion, scalar multiplication and matrix multiplication, Maple requires \+
the command " }{TEXT 261 5 "evalm" }{TEXT -1 2 " (" }{TEXT 262 4 "eval
" }{TEXT -1 7 "uate as" }{TEXT 272 2 " m" }{TEXT -1 177 "atrix).  Furt
hermore, matrix multiplication is denoted by &* and not just *.   Exec
ute the following commands.  Make sure you understand the command and \+
the result in each case." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 
"A := matrix([[1,0,2],[2,3,-1],[4,-2,5]]);\nB := matrix([[-3,1],[1,0],
[9,5]]);\nC := matrix(3,3,(i,j)-> i-j);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "evalm(2*B);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 11 "evalm(A+C);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(
A&*B);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(B&*A);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalm(A^3);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "A1 := inverse(A);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 15 "evalm(A&*(A1));" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 11 "inverse(C);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "transpose(B);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 25 "evalm(B&*transpose(B)); \n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 265 "" 0 "
" {TEXT 264 9 "Exercises" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 22 "A := diag(0,1,2,3,4);\n" }}}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "A := matri
x([[1,2,-1],[3,7,-10],[7,16,-21]]);\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 86 "A := matrix(3,3,[1,0,-1,3,4,-2,3,5,-2]);\nB :
= matrix(3,3,[-1,0,1,1,2/3,-4/3,0,-1,1]);\n" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "P := matrix([[.70
,.05,.10,.20],\n             [.10,.60,.20,.10],\n             [.10,.20
,.50,.10],\n             [.10,.15,.20,.60]]);\n" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "
X := matrix(4,1,[5500,4800,4100,5250]);\n" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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