Suppose the Leslie matrix is 0 0 6a3 L= 1/2 0 0 , a>0. 0 1/3 0 The only reproductive age class is the third age class. (a) [9 points) Find the characteristic equation, eigenvalues, and inherent net reproductive number R of L (b) (4 points] Show that L. is imprimitive. (c) (6 points] For a 1 and X(0) = (6,0,0), find X(1), X(2), X(3); then describe the behavior of X(t) as too. (d) (6 points] For a = 1 and X(0) = (12,2,1)", find X(1), X(2), X(3); then describe the behav- ior X(t) as to.