How do you solve the system z(t+1)=Az(t)+b where A is a 2x2 matrix and z(t+1), z(t), b are 2x1 matricies? I solved the homogeneous solution: z(t)=P(D^t)(P^-1)z(0) where D is the diagonal matrix of eigenvalues of A and P is the matrix of eigenvectors. I tried to solve the nonhomogeneous solution at the steady state where z(t+1)=z(t). I'm not sure if this is the right method. Then I added the two solutions z(t) for the homogeneous and the nonhomogeneous equations.