Is u + v in U if u and v are elements of V but not in U?

[zenn]

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.

 

[eastside00_99]

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.