Final answer:
If the set W is a vector space, a set S of vectors that spans it can be found. If not, it cannot be spanned by a set of vectors.
Step-by-step explanation:
If the set W is a vector space, then a set S of vectors that spans it can be found. In order for a set of vectors to span a vector space, every vector in that space can be written as a linear combination of the vectors in the set S.
For example, if the vector space W is defined as W = (x, y) , then a set S that spans it can be S = {(1, 0), (0, 1)}, because any vector (x, y) in W can be written as a linear combination of (1, 0) and (0, 1) as (x, y) = x(1, 0) + y(0, 1).
If the set W is not a vector space, then it cannot be spanned by a set of vectors.