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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 258 13 "Markov Chains" }}{PARA 0
"" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA
0 "" 0 "" {TEXT 259 27 "Part 1. Television Viewers" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "Our guess about
the eventual distribution \nof television viewers:" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Enter the matri
x " }{XPPEDIT 18 0 "A" "6#%\"AG" }{TEXT -1 16 " and the vector " }
{XPPEDIT 18 0 "p[0" "6#&%\"pG6#\"\"!" }{TEXT -1 1 "." }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 0 "> " 0 ""
{MPLTEXT 1 0 71 "A:=matrix(2,2,[0.85, 0.05,\n 0.15, 0.95
]); \np0:=[0.4,0.6];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA
0 "" 0 "" {TEXT 256 20 "Part 2. Rental Cars" }}{PARA 0 "" 0 "" {TEXT
-1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Enter the matrix " }
{XPPEDIT 18 0 "M" "6#%\"MG" }{TEXT -1 16 " and the vector " }{XPPEDIT
18 0 "p[0" "6#&%\"pG6#\"\"!" }{TEXT -1 3 ". " }}}{EXCHG {PARA 0 "> "
0 "" {MPLTEXT 1 0 83 "M:=matrix(3,3,[.8, .3, .2,\n .1, .
2, .6,\n .1, .5, .2]); " }}{PARA 0 "> " 0 "" {MPLTEXT 1
0 12 "p0:=[0,1,0];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 95 "Repeat your calculations for a car
starting at location 1 and for a car starting at location 3." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 123 "Find the r
educed row echelon form of M-I, first using the rref command and then \+
by performing row operations one at a time." }}}{EXCHG {PARA 0 "> " 0
"" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 338 "IMPORTANT \+
OBSERVATION: Because of rounding error, Maple may incorrectly row red
uce a matrix with decimal entries. By using fractions, we eliminate r
ounding error and Maple will row reduce correctly. Verify this observ
ation by finding the row reduced echelon form of the matrix M - I (whe
re the entries of M are expressed by fractions)." }}}{EXCHG {PARA 0 ">
" 0 "" {MPLTEXT 1 0 101 "M:=matrix(3,3,[8/10, 3/10, 2/10,\n \+
1/10, 2/10, 6/10,\n 1/10, 5/10, 2/10]);\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 ""
{TEXT -1 239 "When you compute the powers of M requested in Step 5, yo
u may wish to re-execute the command which defines M with decimal entr
ies. Alternatively, you may use the evalf command to convert the entr
ies of a matrix from fractions to decimals." }}}{EXCHG {PARA 0 "> " 0
"" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA
0 "" 0 "" {TEXT 260 33 "Part 3. Positive Markov Matrices" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Enter the \+
matrix " }{XPPEDIT 18 0 "A" "6#%\"AG" }{TEXT -1 16 " and the vector "
}{XPPEDIT 18 0 "p[0" "6#&%\"pG6#\"\"!" }{TEXT -1 1 "." }}{PARA 0 "" 0
"" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "A:=matri
x(2,2,[0, 1,\n 1, 0]); \np0:=[0.4,0.6];" }}}{EXCHG
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 16 "Part 4. \+
Summary" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 0 "" }}}}{MARK "27" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }