Finding the nth term in a recursive coupled equation. I'm probably missing something simple, but if I have the recursive sequence:
$$
a_{i+1} = \delta a_i+\lambda_1 b_i
$$
$$
b_{i+1} = \lambda_2 a_i + \delta b_i
$$
how would I find a formula for $a_n$, $b_n$, or even $\frac{a_n}{b_n}$, given, for example, $a_0 = 1$, $b_0=0$?
I've tried expanding it out and looking for patterns but to no avail - I'm sure there must be an analytic solution to this, I really would rather not do it computationally!

You should find a way to write the problem as a matrix problem and then to reduce the matrix to a simpler form.
