Does the problem say "coset" or "subset"? If it really says "coset" (a term I am more familiar with in group theory) how does your text define "coset"?
What you give in your second post, I would call a "linear manifold", not a "coset" but I think I see how that term would fit. The set of vectors with the single operation of "vector addition" is a group and subspace is a subgroup of that group. A fixed vector added to that subgroup is no longer a subgroup (nor a subspace) but is a "linear manifold" which could reasonably be called a "coset". If that is the definition your text gives, then, yes, that is correct.
