Which of the following are vector spaces?

(a) The set of all continuous functions on the interval .

(b) The set of all non-negative functions on the interval .

(c) The set of all polynomials of degree exactly .

(d) The set of all symmetric matrices, i.e. the set of matrices such that .

So (a) is not a vector space because there is no vector?

(b) is a vector space.

(c) is not a vector space.

(d) is a vector space.

Are these correct?