Problem 3. We say that a matrix A e M. (R) is row-stochastic (respectively, column- stochastic) if it is a nonnegative matrix and that additionally, its rows (respectively, columns) all sum to 1. In the following, we assume that A e M, (R) is row-stochastic. (a) Sketch the situations that can occur in terms of the Gershgorin disks of A as provided by Theorem 1. (b) What does the Perron-Frobenius theorem (Theorem 2) say about the situation? (c) Show that (1, (1, ..., 1)?) is an eigenpair of A. (d) Is 1 the spectral radius of A? [In other words, what additional information would you need to conclude?]