- #1
Lolsauce
- 23
- 0
Homework Statement
Find the long-term behavior of the Markov system described by the following matrix with initial conditions below: (i.e. find T^infinity)
Find x_infinity
Homework Equations
x_0 = [.3 .3 .4]^TT =
[.5 .4 .1]
[.4 .3 .3]
[.1 .3 .6]
The Attempt at a Solution
So in my attempt to find x_infinity I know that x_n = ( T^n)(x_0)
This means:
[.5^n .4^n .1^n] * [.3 .3 .4]^T
[.4^n .3^n .3^n]
[.1^n .3^n .6^n]
Which I solved to be
[ .3*.5^n .3*.4^n .4*.1^n]
[ .3*.4^n .3*.3^n .4*.3^n]
[ .3*.1^n .3*.3^n .4*.6^n]
But as n approaches infinity all the terms get smaller and all go to zero. Does this seem correct so far?
That would mean:
x_infinity = ( 0 0 0 )^T ? I tried this on my webassign, but it is not correct. Any tips or help in pointing out my mistakes would be great, thanks!
Last edited: