Question: Assume V is a vector space over a field F, N is a finite nonempty set, and {vn}nN is a sequence of vectors in V.

Assume V is a vector space over a field F, N is a finite nonempty set, and {vn}nN is a sequence of vectors in V. Let V : FN V be the synthesis operator of {vn}nN , that is, for each x FN V(x) = X nN x(n)vn. Show that for any subspace X of FN, the set V(X) = {V(x) : x X} is a subspace of V

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