Let

V be 'n' dim vector space

f1, f2, f3,..,fm be linear function on V (i.e. belong to dual space of V, V* = Hom(V,F))

W1, W2,....Wm be null-spaces of f1, f2,....f3 respectively.

W = Intersection of (W1,W2,..,Wm)

Consider

1. Annihilator of (W) i.e. {f | f belongs to V* and f(W) = 0}

2. F = sub-space of V* spanned by {f1,f2,f3....fm}

I want to show that Annihilator of (W) = F

Please help. Thanks