We can show that, for an n n stochastic matrix, 1 = 1 is an eigenvalue and the remaining eigenvalues must satisfy |j| 1 j = 2, ... , n (See Exercise 24 of Chapter 7, Section 4.) Show that if A is an n n stochastic matrix with the property that Ak is a positive matrix for some positive integer k, then |j| < 1 j = 2, ... , n

3.2 The Mean Value Theorem &Rolle's Theorem The MeanValue Theorem Letf be a function that satisfies the following: 1. f is continuous on the interval [a, b] 2. f is differentiable on the i(a, b)l Then there is a numbcin a,b)such that: f'(c) = f(bf(a) b-a Rolle's Theorem Letf be a function that satisfies...