3. Let V and W be n and m dimensional F-vector spaces and let B and A be bases for V and : W respectively. Let YB: VF and YA W Fm denote the coordinate isomorphisms. Let S: VW be a linear transformation. (a) Prove that yg maps Ker S onto null[S] and YA maps imS onto col[S]. 2 (b) Conclude that null[S] (ker S) and col[S] imS are isomorphisms. (c) Write a statement that connects rank and nullity of [S] to the kernel and image of S.