0.7 b. If the initial state is x0) =| 0.05 , find the nth state x"). 0.25 c. Find lim x"). n00 lim x") n00

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the transition matrix
0.5
3
1
0.5
0.5
3
3
P =| 0.333333
0.166667 0.5 0.166667
0.333333
2
1
3
1
a. Find the eigenvalues and corresponding eigenvectors of P.
The eigenvalue 21 = -1/3
corresponds to the eigenvector v = <0, -1, 1>
The eigenvalue 22 = 0
corresponds to the eigenvector v, = <1,0,-1>
The eigenvalue 23 = 1
corresponds to the eigenvector v3 = <2,1,1>
0.7
b. If the initial state is x0) =| 0.05 |, find the nth state x").
0.25
x(m)
c. Find lim x").
n00
lim x") =
n00
Transcribed Image Text:Consider the transition matrix 0.5 3 1 0.5 0.5 3 3 P =| 0.333333 0.166667 0.5 0.166667 0.333333 2 1 3 1 a. Find the eigenvalues and corresponding eigenvectors of P. The eigenvalue 21 = -1/3 corresponds to the eigenvector v = <0, -1, 1> The eigenvalue 22 = 0 corresponds to the eigenvector v, = <1,0,-1> The eigenvalue 23 = 1 corresponds to the eigenvector v3 = <2,1,1> 0.7 b. If the initial state is x0) =| 0.05 |, find the nth state x"). 0.25 x(m) c. Find lim x"). n00 lim x") = n00
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