(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

x_0 = [.3 .3 .4]^T

T =

[.5 .4 .1]

[.4 .3 .3]

[.1 .3 .6]

3. 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!

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# Homework Help: Finding long term Markov behaviors

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