I have this problem, and could only get part way through before I got stuck. Here it is.

Solve the given system subject to the initial condition.

X'=|2 4| X, X(0) = |-1|

---|-1 6| --------- |6 |

I already solved for lambda (4 and 4), and their eigenvectors (2,1 and 2,1), but I'm stuck after this point. Any help?