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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A: A detailed solution is given below.