Originally Posted by

**alexandrabel90** how do you prove this theorem?

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

then

v+w=a1v1+..+amvm+b1w1+...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?

thanks!