Solve this simultaneous pair of recurrences using diagonalisation Not sure what would be related equations to this. Originally I had no idea how to do this, I set up the first matrix, like this. Then, from there, I know that I have to let: x_k= [[c_k][d_k]]. Then x_k = A^k x_0,so you want powers of A. If you find its eigenvectors, then A = P * [[lambda_1, 0 ] [ 0, lambda_2]] * P^-1, so A^k is P*[[lambda_1^k, 0 ] [ 0, lambda_2^k]]*P^-1. I just don't understand the syntax in this and how to put it to paper Please give me a push in the right direction, I've been stuck on this problem all day.