Question on vectorspace
Let V be a vector space over the field F.
a)Let S be any set of vectors in V , and let W be the intersection of all
subspaces of V which contain S (that is, x ¸ W if and only if x lies in
every subspace which contains S). Prove that W is the set of finite
linear combinations of vectors from S.
My idea is that as long as we show W=spans(s) then the problem is solved.
but how to proof S is the spanning set of W ?????
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