Consider the Leslic population model described in class where a population is divided in n age- classes (ordered so that i = 1 are newborns and in are elderly) and (k) denotes the number of individuals in age-class i at time k. At every time period k each of the zi (k) individuals produces a, offsprings (a, 20 fertility rate) progress to the next age class with survival rate [0.1] leading to the dynamics 2(k+1) x2(k+1) x(k+1) = x3(k+1) an(k+1) = 01 CX2 *** an-1 CX B 0 0 0 0 0 0 3-1 0 Leslie matrix 1 x(k) x3(k) = Ax(k) Assume that o, 20 and 12 8 20 for all i. 1. Find necessary and sufficient conditions on a.; so that the Leslie matrix is irreducible. (2p) 2. For an irreducible matrix as in the previous point find a sufficient condition on the parameters , 3, that ensures that the population will not get extinct. (1p)