I'd like to get some help proving the statement by using a contrapositive statement.
However, whenever I work on this proof, I always get stuck with showing $V$ or $W$ is infinite-dimensional.
Do I have to consider $Tv=0$ case to do it? for some $v \in V$.
If anybody can give me a hint proving this contrapositive statement, it would be really appreciated. I just want to widen my knowledge by proving something in different ways.