Deducing that there exists a subspace U of V and a of V such that M=U+a

Hi, I have the following problem I have been stuck on for the last couple of hours :(... Thanks for any help you can give me!

It says:

"Let be an affine subset of .

Q1 (already solved)

Prove that is affine for every and that, if , then is a subspace.

Q2 (the one I am stuck on)

Deduce that there exists a subspace of and such that

----> this is formula (1)

[Hint: what can be said about such an , assuming that it exists?]

Show further that the subspace in (1) is uniquely determined by and describe the extent to which is determined by ."

And other details regarding the problems in this part of the project are:

"Throughout Part A of this project, will be a real vector space and, for a non-empty subset of and , the set { } will be denoted by .

An affine subset of is a non-empty subset of with the property that whenever and ."