5. Let P be the transition matrix of a Markov chain with finite state space. Let I be the identity matrix, U the |S| x |S| matrix with all entries unity, and 1 the row |S|-vector with all entries unity. Let л be a non-negative vector with Σ; i = 1. Show that лP = if and only if (I-P+U) = 1. Deduce that if P is irreducible then = 1(I-P + U)-¹.

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