Subspace question

  • Thread starter zenn
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  • #1
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Main Question or Discussion Point

Not sure how to prove the following:

If U is a subspace of a vector space V, and if u and v are elements of V, but one or both not in U, can u + v be in U?

Any help would be appreciated.
 

Answers and Replies

  • #2
v=-u

so, if u is not in U, then v=-u is not in U. But, u+v=0 is in U. The other case is false --- i.e., if u+v is in U and u is in U, then v has to be in U also. You should prove that yourself though.
 

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