how do you prove this theorem?
let S be a subset of a vector space V
(a) Then span S is a subspace of V which contains S
(b) if W is a subspace of V containing S, then span s ⊆ W
i would think that,
assume v, w ∈ span S, where
v= a1va + a2v2+...+ amvm and w=b1w1+b2w2+...bmwm
thus span S is a linear combination of the vectors in S.
does that show that it is a subspace of V? it seems to me that i have just proven that span S is a vector space....
then how do i do the second part?