For a vector space V and a finite set of vectors S = {v1, ..., vn} in V, copy down the definitions for:
(a) span(S)
A) Span(S) is the set of all linear combinations of vectors in S.
B) Span(S) is the set of all vectors in V.
C) Span(S) is the set of all scalar multiples of the vectors in S.
D) Span(S) is the set of all orthogonal vectors to S.
(b) a basis for V
A) A basis for V is a linearly independent set that spans V.
B) A basis for V is any subset of V.
C) A basis for V is the set of all vectors in V.
D) A basis for V is a set of orthogonal vectors in V.
(c) a subspace of V
A) A subspace of V is any subset of V.
B) A subspace of V is the set of all vectors in V.
C) A subspace of V is a set of linearly independent vectors in V.
D) A subspace of V is a non-empty subset of V.