I have the following question: I have been thinking about this for a while now, but I simply cannot work it out...

Let V be a linear space of n dimensions over R, and let S,T:V->V be linear transformations.

True or False?

1. If v is an eigenvector of S and of T, then v is also an eigenvector of S + T.

2. If Î»_1 is an eigenvalue of S and Î»_2 is an eigenvalue of T, then Î»_1 + Î»_2 is a eigenvalue of S + T.

I am not just looking for the right answer, but also for the reasoning behind it...

Thank you!