I am supposed to solve the discrete dynamical system _k+1=A*x_k, and I have been given both the matrix A and x_O (please see the picture below). I started out by calculating the eigenvalues and then their eigenvectors, so that I have lambda, and could then get the weights for c1 and c2 by putting the eigenvectors on the right-hand side and x_0 on the left-hand side. However, my answer seems to be wrong. Does anyone see where in my calculations I messed up?
Many thanks, Nick