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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.