To show is a subspace you need to prove then . Next you need to prove that if and (the field you are working over) thenLet V and W be vector spaces, and let S be a subset of V. Define S^0 = {T Є L (V,W): T(x) = 0 for all x Є S}. Prove the following statements:

a) S^0 is a subspace of L(V,W)

To show you need to show if then .b) If S1 and S2 are subsets of V and S1 is contained in S2, then S2^0 is contained in S1^0

This is straightforward.