Linear Algebra - Affine subsets, proving M = U + a is unique

[Upsidealien]

Homework Statement

Let M be an affine subset of V.

We then prove that if 0 ∈ M then M is a subspace.

There exists a subspace U of V and a ∈ V such that
M = U + a. (1)

Show that the subspace U in (1) is uniquely determined by M and describe the extent to which a is determined by M.

Homework Equations

An affine subset of V is a non-empty subset M of V with the property that λx+(1−λ)y ∈ M whenever x,y ∈ M and λ ∈ R.

The Attempt at a Solution

Not sure.

 

[micromass]

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