Question: How do I solve the system Pq = q where P is a transition (stochastic) matrix and q the steady state vector

First, I want to find the set of solutions of this system and then find the steady state vector.

I know that I can find an approximation of the steady state vector ''directly'' if I calculate Pfor big k values (one column of Pk will give me an approximation), but it's not what I want to do. I need the complete set of solutions with a free parameter.

LinearSolve() doesn't give me the set of solutions. See the picture below. Here Q is the transition matrix.

I hope my question is clear (:

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