Thread: 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.

Originally Posted by ruprotein

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.
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An alternate way to think of it is like this. are subspaces, thus, they are abelian groups under vector addition (definition of vector spaces). Thus, by the conditions of the problem 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 is an abelian group under addition of vectors follows that one of them is contained in the other. Thus, or

You can also see a proof here.