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Math Help - PROOF sUBpace problem

  1. #1
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    PROOF sUBpace problem

    can some one solve this ?

    Let W1 and W2 be subspaces of a vector space V. Prove that W1 union W2 is a subspace of V iff one of the subspaces contains the other.
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  2. #2
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    Quote Originally Posted by ruprotein View Post
    can some one solve this ?

    Let W1 and W2 be subspaces of a vector space V. Prove that W1 union W2 is a subspace of V iff one of the subspaces contains the other.
    The only if part is trivial. Here http://www.mathhelpforum.com/math-he...oup-proof.html, try to understand it. The proof to your problem is almost exactly the same.
    ---
    An alternate way to think of it is like this. W_1,W_2 are subspaces, thus, they are abelian groups under vector addition (definition of vector spaces). Thus, by the conditions of the problem W_1<br />
\cup W_2 is a subspace and hence an abelian group. The link I gave you says, the union of two subgroups is a subgroup if and only if one is contained in the other. Now since W_1<br />
\cup W_2 is an abelian group under addition of vectors follows that one of them is contained in the other. Thus, W_1\subseteq W_2 or W_2\subseteq W_1
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  3. #3
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    You can also see a proof here.
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