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{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 
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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "MAPLE ASIIGNMENT 6" }}
{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 62 "The arithmetic operations for matrices are + , - , &* , ^
 .The" }}{PARA 0 "" 0 "" {TEXT -1 69 "following shows how Maple calcul
ates a determinant. You can of course" }}{PARA 0 "" 0 "" {TEXT -1 36 "
put any numbers that you like into M" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 37 "M:=matrix(3,3,[1,0,-1,3,6,2,3,-3,1]);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 7 "det(M);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "The
 next command allows you to check that you can calculate a 3X3" }}
{PARA 0 "" 0 "" {TEXT -1 49 "determinant by hand. Fill in the 4 missin
g terms." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "(1*6*1)-((-1)*6*3)" }}
{PARA 0 "" 0 "" {TEXT -1 70 "Diagonal matrices are created with the di
ag command.  This can be used" }}{PARA 0 "" 0 "" {TEXT -1 29 "to creat
e an identity matrix." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "iden:=diag
(1,1,1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "Inverse matrices are \+
either M^(-1)  or inverse(M).  The following" }}{PARA 0 "" 0 "" {TEXT 
-1 37 "calculate the inverse, check that it " }}{PARA 0 "" 0 "" {TEXT 
-1 50 "works and illustrate the properties of inverses.  " }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 11 "M1:=M^(-1);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "evalm(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
18 "evalm(M&*M1-iden);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "e
valm(M1&*M-iden);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalm(
M1^(-1));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "To check that you un
derstand how to calculate the inverse matrix by" }}{PARA 0 "" 0 "" 
{TEXT -1 69 "hand replace the ? in the command below by appropriate en
tries from M" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalm(M);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "M1??:=((-1)^?)*det(matrix(2,
2,[?,?,?,?]))/det(M);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalm(M1);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 69 "The next commands illustrate the correct \+
and the incorrect way to get" }}{PARA 0 "" 0 "" {TEXT -1 43 "the inver
se of the product of two matrices." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
16 "M2:=evalm(M+M1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "eva
lm((M&*M2)^(-1));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "evalm(
(M2^(-1))&*(M^(-1)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "ev
alm((M^(-1))*(M2^(-1)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 
"evalm((M^(-1))+(M2^(-1)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
19 "evalm((M+M2)^(-1));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "The la
st two commands have illustrated a dumb artihmetical mistake you" }}
{PARA 0 "" 0 "" {TEXT -1 34 "should not make even with numbers." }}
{PARA 0 "" 0 "" {TEXT -1 26 "PROPERTIES OF DETERMINANTS" }}{PARA 0 "" 
0 "" {TEXT -1 68 "The commands below check some of the properties of d
eterminants. You" }}{PARA 0 "" 0 "" {TEXT -1 67 "should look to see th
at the new matrices being created are what you" }}{PARA 0 "" 0 "" 
{TEXT -1 18 "expect them to be." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "e
valm(M);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "M3:=transpose(M
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "det(M3);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "M4:=swaprow(M,1,3);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "det(M4);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 20 "M5:=swapcol(M4,1,2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "det(M5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 
"M6:=mulrow(M5,3,0.3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "de
t(M6);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "det(M5)*0.3;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "M7:=mulcol(M6,2,3);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "det(M7);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 10 "det(M6)*3;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "M8:=addrow(M7,1,3,.5);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "det(M8);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 
"M9:=addcol(M8,3,2,1.5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "
det(M9);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "A matrix with two ide
ntical rows or two identical columns has a zero" }}{PARA 0 "" 0 "" 
{TEXT -1 70 "determinant. Change the ? below to create such a matrix a
nd then check" }}{PARA 0 "" 0 "" {TEXT -1 18 "this property out." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "M10:=matrix(3,3,[?,?,?,?,?,?,?,?,?]
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "det(M10);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 30 "M1 was the inverse matrix of M" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 7 "det(M);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "det(M1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "The d
eterminant of the product is the product of the determinants." }}
{PARA 0 "" 0 "" {TEXT -1 38 "This does not work with sums however. " }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "det(M&*M9);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 15 "det(M)*det(M9);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "det(M+M9);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
15 "det(M)+det(M9);" }}}}{MARK "0 3 0" 13 }{VIEWOPTS 1 1 0 1 1 1803 }