Question: a) Given a stochastic matrix A with non-negative entries whose row sums are equal to 1, which also satisfies the Perron-Frobenius assumptions. Its invariant

a) Given a stochastic matrix A with non-negative entries whose row sums are equal to 1, which also satisfies the Perron-Frobenius assumptions. Its invariant distribution is its unique left eigenvector. Find the unique left eigenvector and then compute its derivatives with respect to a. 0.6+ a 0.4- a 0.2 0.8 a 20 b) Given A is any stochastic matrix of mixing , is a small pertubative parameter. Can we find the unique left eigenvector and then compute its derivatives with respect to a?

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