Spanning Sets Proposition Suppose v1,v2.....Un are vectors in V.Then S(v1,v2,...,Un)is a subspace of V. Proof. S is closed under c1v1+c22+..+cnm+d11+d22+..+dnn= =(c1+d)v+(c2+d2)2+.+(cn+dn)vn. S is closed under. c(c1v1+c2v2+...+cnUn)=(cc1)v1 +(cc2)v2+...+(ccn)Un. S(v1,v2,...,Un)is said to be the subspace of V spanned by U1,U2,·,UnSpanning Sets Proposition Suppose v1, v2, . . ., vn are vectors in V . Then S (v1, v2, . . . , vn) is a subspace of V . Proof. S is closed under + c1v1 + c2v2 + . . . + cnvn + d1v1 + d2v2 + . . . + dnvn = = (c1 + d1)v1 + (c2 + d2)v2 + . . . + (cn + dn)vn. S is closed under • c(c1v1 + c2v2 + . . . + cnvn) = (cc1)v1 + (cc2)v2 + . . . + (ccn)vn. S (v1, v2, . . . , vn) is said to be the subspace of V spanned by v1, v2, . . . , vn