1) Suppose is a subspace. Then by definition, W is closed under addition, scalar multiplication. Then in particular, all linear combinations of vectors in S are in W... Also note S is contained in span(S).

2) What is the definition of the span? It's the set of all linear combinations of the vectors, no? Then what can we say about sums? Scalar multiples?

3) Let . Then x is some linear combination of vectors in , so in particular is a linear combination of vectors in S_1 and a linear combination of vectors in S_2...