finding $dim\{T\in hom(V,W)|Im(T)\subseteq Z\}$ $Z\subseteq W$

Question

I'm having trouble solving the following:

Suppose $V,W$ are vector spaces of a finite dimension over $\Bbb F$ and $Z$ is a subspace of $W$

Say $A = \{T\in hom(V,W)|Im(T)\subseteq Z\}$

Iv'e managed to prove $A$ is in fact a subspace of $hom(V,W)$ but cannot figure out how to calculate its dimension using the dimensions of $V,W,Z$.

Any help would be appreciated

Answer 1

Hint:

Show that $ \dim A= \dim hom(V,Z)$