Let V and W be vector spaces with ordered bases E and F, respectively. If L : V → W is a linear transformation and A is the matrix representing L relative to E 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.
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