Let V, W be vector spaces with ordered bases F and F, respectively. If L : V

Question:

Let V, W be vector spaces with ordered bases F and F, respectively. If L : V → W is a linear transformation and A is the matrix representing L relative to F and F, show that
(a)v ∈ ker(L) if and only if [v]E ∈ N(A).
(b)w ∈ L(V) if and only if [w]f is in the column space of A