# Math Help - Prove zero vector

1. ## Prove zero vector

Let $\lambda$ and $\mu$ be distinct eigenvalues for $T:R^n-->R^n$and let the corresponding eigenspaces be $V_\lambda$ and $V_\mu$ respectively. Prove that the only vector common to both $V_\lambda$ and $V_\mu$ is the zero vector.

2. What do you get if you apply T to a vector lying in the intersection?

3. Look at this topic:

http://www.mathhelpforum.com/math-he...ro-vector.html