Let A be a non negative, irreducible matrix such that I A is invertible and (I A) 1 O Let 1 and v 1 be the Perron root and Perron eigenvector of A (a) Prove that (b) Deduce from (a) that v 1 Av 1

Question: Let A be a non-negative, irreducible matrix such that I - A is invertible and (I - A) -1 O. Let 1 and

Let A be a non-negative, irreducible matrix such that I - A is invertible and (I - A)^-1 ≥ O. Let λ₁ and v₁ be the Perron root and Perron eigenvector of A.
(a) Prove that .
(b) Deduce from (a) that v₁ Av₁.

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