5. Let V, W be finite dimensional vector spaces over K. Let $n = \text{dim } V$ and $m = \text{dim } W$.
(a) Let $\mathcal{B}, \mathcal{B}'$ be bases of V, W respectively. Prove that the assignment
$F \mapsto M_{\mathcal{B}}^{\mathcal{B}'}(F)$
is an isomorphism from $\mathcal{L}(V, W)$ to the vector space of $m \times n$ matrices in K.
(b) What is the dimension of $\mathcal{L}(V, W)$ in terms of m and n?
