1. The problem statement, all variables and given/known data Prove that if T, S : V -> W are linear and W is finite dimensional then dim (range(S + T)) <= dim range S + dim range T 2. Relevant equations 3. The attempt at a solution I know that the dim range S + dim range T can be at most 2 * dim W. However, I'm a little stuck on trying to figure out what dim (range(S+T)) is. How do I determine S + T?