How Do You Calculate Long-Term Proportions in a Markov Chain?

[musad]

Not really sure how to get started on this one:Find the long-term proportions, a and b, of the two states, A and B, corresponding to the transition matrix T=|0.7 0.4|
| 0.3 0.6|

Note, the matric is a 2x2 matrix

Thanks

 

[pickslides]

Consider the nth state of a,b to be given by $s_n = T^n \times s_0$

For long term convergence try n = 50 and n=100, if they do not vary then you have your answer.

The only bit we are missing is $s_0$ were you given that? If not try some scenarios i.e. $a=b=0.5$