1. The problem statement, all variables and given/known data 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. 2. Relevant 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. 3. The attempt at a solution Not sure.