There is a question in the final exam that says: "(c) For what initial conditions u(0) does the solution u(t) to this differential equation lie on a single straight line in R2 for all t?"

In the solution is says that when u(0) is equal to one of the two eigenvectors. Why is it that? I know u(0)=Sc where c is the diagonal matrix but I can't make that connection needed to answer the question...

Edit: I forgot to mention that u(t) is 2 by 1.

Question

There is a question in the final exam that says: "(c) For what initial conditions u(0) does the solution u(t) to this differential equation lie on a single straight line in R2 for all t?"

In the solution is says that when u(0) is equal to one of the two eigenvectors. Why is it that? I know u(0)=Sc where c is the diagonal matrix but I can't make that connection needed to answer the question...

Edit: I forgot to mention that u(t) is 2 by 1.