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## Homework Statement

Let U

_{1}and U

_{2}be subspaces of a vector space V.

Let U be the set of all vectors of the form

**u**+

_{1}**u**, where

_{2}**u**is a member of U

_{1}_{1}and

**u**is a member of U

_{2}_{2}.

Show that U is a subspace of V.

## Homework Equations

U inherits it's operations from V (through U

_{1}and U

_{2}) and so we have to show that scalar.mult and vec.add are closed for U.

a(b

**v**)=(ab)

**v**

a

**v**+ b

**v**= (a+b)

**v**

## The Attempt at a Solution

Since U

_{1}and U

_{2}are a subset of V, then adding any

**u**to

_{1}**u**may not be closed wrt either U

_{2}_{1}or U

_{2}but I think they should be closed wrt V. Intuitively that seems true but I get stuck trying to be more concrete than that.