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{SECT 0 {EXCHG {PARA 3 "" 0 "" {TEXT 256 28 "Elementary Matrix Operati
ons" }}{PARA 0 "" 0 "" {TEXT -1 54 "This worksheet shows how to enter \+
matrices and how to " }}{PARA 0 "" 0 "" {TEXT -1 37 "perform basic ope
rations on matrices." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "First loa
d the linear algebra package.  The colon suppresses output." }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{SECT 1 {PARA 3 "" 0 "
" {TEXT -1 16 "Entering Matrics" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 
"There are several ways to enter matrices.  In what follows A and C" }
}{PARA 0 "" 0 "" {TEXT -1 66 "are entered as lists of lists.  The matr
ix B is entered using the " }{TEXT 257 6 "matrix" }}{PARA 0 "" 0 "" 
{TEXT -1 66 "command with three parameters.  The first two parameters \+
give the " }}{PARA 0 "" 0 "" {TEXT -1 73 "size of the matrix and the t
hird is a single list of the elements.  Note " }}{PARA 0 "" 0 "" 
{TEXT -1 46 "the order of the elements in the final matrix." }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 90 "A := matrix([[1,2],[2,3]]);\nB := matrix(
2,2,[3,-1,0,3]);\nC := matrix([[1,0,-1],[2,3,-5]]);" }}}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 34 "Matrix Addition and Multiplication" }}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 15 "Matrix Addition" }}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 69 "There are two basic ways to do matrix addition.
 The first is with the" }}{PARA 0 "" 0 "" {TEXT -1 35 "addition operat
or, + or &+, and an " }{TEXT 258 5 "evalm" }{TEXT -1 26 ".  If one doe
s not use the" }}{PARA 0 "" 0 "" {TEXT 259 5 "evalm" }{TEXT -1 33 ", M
aple will not compute the sum." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "e
valm(A + B);\nevalm(A &+ B);\nA + B;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 4 "The " }{TEXT 261 6 "matadd" }{TEXT -1 24 " command is part of th
e " }{TEXT 262 6 "linalg" }{TEXT -1 26 " package.  One can include" }}
{PARA 0 "" 0 "" {TEXT -1 30 "coeffiecients to the addition." }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 29 "matadd(A,B);\nmatadd(A,B,1,a);" }}}}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 21 "Matrix Multiplication" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 74 "As with addition, there are two basic way
s of doing matrix multiplication." }}{PARA 0 "" 0 "" {TEXT -1 32 "One \+
is with the &* operator and " }{TEXT 260 5 "evalm" }{TEXT -1 1 "." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalm(A &* C);" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 26 "The other way is with the " }{TEXT 263 8 "multiply
" }{TEXT -1 39 " command from the linalg package.  With" }}{PARA 0 "" 
0 "" {TEXT -1 60 "this command one can multiply more than two matrices
 easily." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "multiply(A,C);\nmultipl
y(A,B,C);\nmultiply(C,A);" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 16 "S
pecial Matrices" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 15 "The Zero Matri
x" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "The " }{TEXT 264 6 "matrix" }
{TEXT -1 73 " command can have a function of the entry indices as the \+
third parameter." }}{PARA 0 "" 0 "" {TEXT -1 51 "Using this form, it i
s easy generate a zero matrix." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "m
atrix(2,2,0);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 19 "The Identity M
atrix" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "The " }{TEXT 265 4 "diag" 
}{TEXT -1 18 " command from the " }{TEXT 266 6 "linalg" }{TEXT -1 53 "
 package takes a sequence of n numbers or expressions" }}{PARA 0 "" 0 
"" {TEXT -1 81 "and returns a diagonal matrix with the sequence elemen
ts on the main diagonal and" }}{PARA 0 "" 0 "" {TEXT -1 30 "zeros in e
very other position." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "diag(1,1);
" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 15 "Random Matrices" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 42 "One can generate random matrices with the
 " }{TEXT 267 10 "randmatrix" }{TEXT -1 18 " command from the " }
{TEXT 268 6 "linalg" }}{PARA 0 "" 0 "" {TEXT -1 76 "package.  This can
 be useful for testing a hypothesis.  This procedure takes" }}{PARA 0 
"" 0 "" {TEXT -1 78 "two parameters, the size of the matrix, and retur
ns a matrix whose entries are" }}{PARA 0 "" 0 "" {TEXT -1 27 "random t
wo digit integers. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "randmatrix(2
,2);" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "There are other specific
 types of matrices that are preprogrammed in Maple." }}{PARA 0 "" 0 "
" {TEXT -1 71 "If you are interested, look at the commands in the lina
lg package using" }}{PARA 0 "" 0 "" {TEXT -1 18 "the help facility." }
}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 16 "Simple Exercises" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 41 "Find the product and sum of the matrices \+
" }{XPPEDIT 18 0 "A =MATRIX([[1,2,3],[4,3,1],[2,0,1]])" "/%\"AG-%'MATR
IXG6#7%7%\"\"\"\"\"#\"\"$7%\"\"%\"\"$\"\"\"7%\"\"#\"\"!\"\"\"" }{TEXT 
-1 5 " and " }{XPPEDIT 18 0 "B = MATRIX([[1,0,-1],[2,-2,2],[3,-1,2]])
" "/%\"BG-%'MATRIXG6#7%7%\"\"\"\"\"!,$\"\"\"!\"\"7%\"\"#,$\"\"#F-\"\"#
7%\"\"$,$\"\"\"F-\"\"#" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 84 "Generate 20 pairs of random 2 by 2 matrices and check if \+
they commute, i.e. CS = SC." }}{PARA 0 "" 0 "" {TEXT -1 71 "What do yo
u conclude about the portion of 2 by 2 matrices that commute?" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Define " }{XPPEDIT 18 0 "D=diag(1,2
,3)" "/%\"DG-%%diagG6%\"\"\"\"\"#\"\"$" }{TEXT -1 5 " and " }{XPPEDIT 
18 0 "G = MATRIX([[1,2,3],[4,5,6],[7,8,9]])" "/%\"GG-%'MATRIXG6#7%7%\"
\"\"\"\"#\"\"$7%\"\"%\"\"&\"\"'7%\"\"(\"\")\"\"*" }{TEXT -1 42 ".  Com
pute DG and GD.  Explain the results" }}{PARA 0 "" 0 "" {TEXT -1 65 "u
sing the sum and row characterizations of matrix multiplication." }}}}
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