This is a Matlab exercise. In the question, there is a vector x0 = [0.1 0.9], which is 2x1 obviously. It asks how many time steps is required to get the steady state vector x's entries all accurate with 3 digits behind the decimal.

My approach to this question was writing a loop on MATLAB executing a markov chain, where I created an arbitrary probability vector P, and ran the loop x = P*x for a certain number of trials. I varied the number of trials and examined the digits of the final result of vector x. I found that for one P matrix, 1 step was all that was required for 3 digits in the steady state vector x. I decided to change P to something else more simplisistic, and I found that 1 step was not enough for 3 digit accuracy. My question is, is 1 step enough to achieve 3 digits, and if so, why is that? Alternatively, what makes it so that it requires more than 1 step (what about P specifically) ?