This is a iterated matrix model problem

1. Consider the iterated matrix model Un+1 = Aun: where the transition matrix is A = 1/3 2/3 1 2/3 (a) The matrix A has eigenvalues A = 4/3 and / = -1/3. The vector 0 = is an eigenvector corresponding to the eigenvalue A = 4/3. Find the corresponding eigenvector for p. Write the general solution un in terms of the eigenvalues and eigenvectors of A (and the unspecified constants a and b). (b) Let uo = 20 0 find the appropriate constants a and b and write out the particular solution for un