In Exercises 1 and 2, consider a Markov chain on {1; 2} with the given transition matrix

Question:

In Exercises 1 and 2, consider a Markov chain on {1; 2} with the given transition matrix P. In each exercise, use two methods to find the probability that, in the long run, the chain is in state 1. First, raise P to a high power. Then directly compute the steadystate vector.