Let V, W be finite-dimensional vector spaces over F. Let L : V → W be a linear map. Suppose U ⊂ V is a non-trivial subspace of V such that U ∩ ker(L) = {0}. Let L|U denote L with its domain restricted to U. (c) Let dimF(V ) = n, dimF(W) = m, dimF(U) = p, and dimF(L(U)) = q. As much as possible, relate the sizes of n, m. P, q. If some of these cannot be related, explain why. Justify. This should include whether L(U) a subspace of W and why. (d) Now suppose L is injective, but not bijective. With this new information, relate the sizes of n, m. P, q. Justify completely.