- #1

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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.

- Thread starter zenn
- Start date

- #1

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If

Any help would be appreciated.

- #2

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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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