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?