Proving Vector Space Relationships in WU{A} and WU{B}

[LAINHELL]

Hi, I need help with this:

Let V be a vector space (V may be infinite) and let W be a subspace of V, if "B" is a vector in V that doesn't belong to W, prove that if "A" is a vector in V such that "B" exists in the subspace WU{A} then "A" exists in the subspace WU{B}.

I also have a question, can a subspace W of an infinite vector space be infinite?

thanks.

 

[Office_Shredder]

Tacking on a single vector (or even a 1-dimensional subspace) onto a subspace via set union doesn't give you another subspace. Your question probably wanted W+<A> where + is vector space addition (all vectors of the form w+a, w in W and a in span{A})