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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "MAPLE ASIIGNMENT 5" }}
{PARA 0 "" 0 "" {TEXT -1 65 "The first command loads the matrix algebr
a operations into Maple." }}{PARA 0 "" 0 "" {TEXT -1 70 "Change the : \+
to ; if you wish to see all the commands in this package." }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 69 "Next define a few matrices. You can change the numbers to
 any numbers" }}{PARA 0 "" 0 "" {TEXT -1 9 "you like." }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 37 "M1:=matrix(3,3,[1,0,-1,1,5,7,3,3,9]);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "M2:=matrix(3,3,[1,0,-1,3,6,2
1,3,3,9]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "The next commands c
reate some other matrices from M1 and M2." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "M3:=submatrix(M2,2..3,1..2);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 28 "M4:=submatrix(M1,2..3,1..3);" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 17 "M5:=stack(M2,M4);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 18 "M6:=concat(M3,M4);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 67 " The next command illustrates multiplication by a scalar.
  Evalm is" }}{PARA 0 "" 0 "" {TEXT -1 32 "needed for the answer to ap
pear " }}{PARA 0 "" 0 "" {TEXT -1 56 "on the screen. Refer back to M6 \+
to see what has happened" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(3
*M6);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 69 "The aritmetic operations for matrices are + , - , &* , ^ \+
. For easier" }}{PARA 0 "" 0 "" {TEXT -1 27 "reference the next comman
d " }}{PARA 0 "" 0 "" {TEXT -1 68 "brings M1 and M2 back on to the scr
een side by side in a 3X6 matrix." }}{PARA 0 "" 0 "" {TEXT -1 17 "Exec
ute the next " }}{PARA 0 "" 0 "" {TEXT -1 63 "command and after you ar
e sure you understand what has happened" }}{PARA 0 "" 0 "" {TEXT -1 
27 "execute the command agaiin " }}{PARA 0 "" 0 "" {TEXT -1 42 "with +
 changed first to - and then to &* ." }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 14 "concat(M1,M2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "eva
lm(M1+M2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "If you wish to chec
k your understanding of matrix multiplication the" }}{PARA 0 "" 0 "" 
{TEXT -1 33 "following command calculates the " }}{PARA 0 "" 0 "" 
{TEXT -1 69 "[2,2] entry of the product matrix. Change the numbers in \+
this command" }}{PARA 0 "" 0 "" {TEXT -1 24 "to calculate some other \+
" }}{PARA 0 "" 0 "" {TEXT -1 68 "entries in the product matrix. If one
 of the numbers is negative put" }}{PARA 0 "" 0 "" {TEXT -1 15 "it in \+
brackets." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "(1*0)+(5*6)+(7*3);" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "The next comand does a power of a
 matrix. You can check the answers" }}{PARA 0 "" 0 "" {TEXT -1 24 "out
 in the same way the " }}{PARA 0 "" 0 "" {TEXT -1 20 "product was chec
ked." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(M1^2);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 68 "The following illustrate some of the prop
erties of matrix algebra. A" }}{PARA 0 "" 0 "" {TEXT -1 30 "matrix is \+
transposed when its " }}{PARA 0 "" 0 "" {TEXT -1 69 "rows and columns \+
are switched..  The properties are the associative ," }}{PARA 0 "" 0 "
" {TEXT -1 29 "commutative and distributive " }}{PARA 0 "" 0 "" {TEXT 
-1 11 "properties." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "M7:=transpose
(M4)&*M4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalm(M4);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalm(M7);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalm((M1+M2)+M7);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalm(M1+(M2+M7));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evalm((M1&*M2)&*M7);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evalm(M1&*(M2&*M7));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "evalm((M1+M2)-(M2+M1));" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 62 "The commutative law does not however work
 with multiplication." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "evalm((M1&
*M2)-(M2&*M1));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "The final prop
erty illustrated here is one of the distributive laws." }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 19 "evalm((M1+M2)&*M7);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 25 "evalm((M1&*M7)+(M2&*M7));" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 70 "Diagonal matrices are created with the diag command.  \+
This can be used" }}{PARA 0 "" 0 "" {TEXT -1 29 "to create an identity
 matrix." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diag(-3,2,Pi); " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "iden:=diag(1,1,1);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "Inverse matrices are either A^(-1)
  or inverse(A).  The following" }}{PARA 0 "" 0 "" {TEXT -1 37 "calcul
ate the inverse, check that it " }}{PARA 0 "" 0 "" {TEXT -1 69 "works \+
and illustrate the properties of inverses.  You should also try" }}
{PARA 0 "" 0 "" {TEXT -1 32 "to calculate the inverse of M2 ." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "M8:=M1^(-1);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 9 "evalm(\");" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "evalm(M1&*M8-iden);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "evalm(M8&*M1-iden);" }}{PARA 11 "" 1 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalm(M8^(-1));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "M9:=evalm(M1+M7);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "The next commands illustrate the c
orrect and the incorrect way to get" }}{PARA 0 "" 0 "" {TEXT -1 43 "th
e inverse of the product of twp matrices." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "evalm((M1&*M9)^(-1));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "evalm((M9^(-1))&*(M1^(-1)));" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 27 "evalm((M1^(-1))*(M9^(-1)));" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 27 "evalm((M1^(-1))+(M9^(-1)));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evalm((M1+M9)^(-1));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 70 "The last two commands have illustrated a dumb artihmetical mist
ake you" }}{PARA 0 "" 0 "" {TEXT -1 34 "should not make even with numb
ers." }}}}{MARK "0 0 0" 16 }{VIEWOPTS 1 1 0 1 1 1803 }