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## 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

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