# Vector Spaces & Subspaces, Linear Algebra

#### kash25

1. The problem statement, all variables and given/known data

Let V be a vector space and U a subspace of V . For a given x ∈ V , deﬁne T=
{x + u | u ∈ U }. Show that T is a subspace of V if and only if x ∈ U .

2. Relevant equations
Subspace Test:
1: The 0 vector of V is included in T.
2: T is closed under vector addition
3: T is closed under scalar multiplication

3. The attempt at a solution
I do not know how to show this...

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#### Dick

Homework Helper
You're not trying very hard. Start with the forward direction. Show T is a subspace if x is in U. Try showing in this case T=U.

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