This is an 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 is an eigenvector corresponding to the eigenvalue A = 4/3. Find the corresponding eigenvector for p. Write the general solution u, in terms of the eigenvalues and eigenvectors of A (and the unspecified constants a and b). (b) Let uo find the appropriate constants a and b and write out the particular solution for un