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Math Help - Linear functions and annihilators

  1. #1
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    Linear functions and annihilators

    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
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  2. #2
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    It is easy to show F is a subset of Annihilator of (W). I am struggling to show the other way round i.e. if x in Annihilator of (W), then x in F i.e. x is spanned by {f1,f2,f3....fm}
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