Question

Let V be a finite dimensional vector space over a field F, and let T :V → V be a linear
transformation. Prove that if V = N(T) + R(T), then N(T) ∩ R(T) = { 0V } (so that
V = N(T)⊕R(T)). Hint: try to identify the subspace of W that is the image of R(T);
that is, T(R(T)).