Prove the following theorem, which could be viewed as a reformulation of parts

Prove the following theorem, which could be viewed as a reformulation of parts   (3) and (4) of Theorem G, or more appropriately as a corollary of Theorem G (Proof Technique LC).

Suppose V is a vector space and S is a subset of V such that the number of vectors in S equals the dimension of V . Then S is linearly independent if and only if S spans V .