Spanning Sets


theorem 4.3.1


if S = {w1 w2 ... wn} is a nonempty set of vectors in a vector space V, then:


(a) The set W of all possible linear combinations of the vectors in S is a subspace of V


(b) The set W in part (a) is the "smallest" subspace of V that contains all of the vectors in S in the sense that any other subspace that contains those vectors contains W



(a) 에서의 W가 뭐에요?


(b) 에서 W가 V의 smallest subspace라 하는데, 왜 smallest 인가여