Question: 8. (Computational) Consider a Markov process with a transition matrix: 0.2 0.4 0.8 0.0 0.3 0.1 0.0 0.3 A = 0.4 0.3 0.1 0.4 0.1

8. (Computational) Consider a Markov process with a transition matrix: 0.2 0.4 0.8 0.0 0.3 0.1 0.0 0.3 A = 0.4 0.3 0.1 0.4 0.1 0.2 0.1 0.3 (a) Use the MATLAB command eig (A) to find the eigenvalues of the Markov matrix. (b) Use the MATLAB command [X, L] = eiga) to find the eigenvectors of the Markov matrix (they will be in the columns of X). (c) Explain why the eigenvectors found in (b) are not probability vectors. (d) Can you find an eigenvector that is a probability vector? Can you find more than one? Explain your answer. (e) Use your answer from (d) to find a stable probability vector, p * = Ap*

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