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Math Help - Help proving a subset is a subspace

  1. #1
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    Help proving a subset is a subspace

    "Let V be a vector space, and let W1 and W2 be subspaces of V. Prove that (W1 ^ W2) is a subspace of V."

    by ^ I mean the intersection of W1 and W2.

    I'm not sure how to do this... (W1 ^ W2) is obviously a subset of V but how do you prove it has closure under vector addition and scalar multiplication?
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  2. #2
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    Closure under vector adition

    u,v\in W_1 \cap W_2
    \Rightarrow u,v\in W_1 \land u,v\in W_2
    \Rightarrow u+v\in W_1 \land u+v\in W_2
    \Rightarrow u+v\in W_1 \cap W_2

    Closure under scalar multiplication (similarly)
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