Yes, W is a subspace in R^3. You can easily check it on your own, that all axioms of a subspace are held. It is a standard routine check (nothing special or interesting). W is a subspace of the dimension 2 in R^3 (since one and only one linear equation determines this subspace). Its basis are these two vectors of R^3 (3,1,0) and (0,0,1).