. a) Show that any set S = {s1, s2, . . . , sm} ⊂ V such that m > n is linearly dependent. b) Let B, B˜ be two distinct basis of V with |B| = p, |B˜| = q. Prove that p = q = n.

Question

Consider V , a real vector space such that dim(V ) = n. a) Show that any set S = {s1, s2, . . . , sm} ⊂ V such that m > n is linearly dependent. b) Let B, B˜ be two distinct basis of V with |B| = p, |B˜| = q. Prove that p = q = n.