When is {x + u | u ∈ U} a subspace of V?

[kash25]

Homework Statement

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 .

Homework 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

The Attempt at a Solution

I do not know how to show this...

 

[Dick]

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.