Which of the following are

vector spaces?

(a) The set of all continuous functions on the interval $\displaystyle [0,1] $.

(b) The set of all non-negative functions on the interval $\displaystyle [0,1] $.

(c) The set of all polynomials of degree exactly $\displaystyle n $.

(d) The set of all symmetric $\displaystyle n \times n $ matrices, i.e. the set of matrices $\displaystyle A = \{a_{j,k} \}_{j,k = 1}^{n} $ such that $\displaystyle A^{T} = A $.

So (a) is not a vector space because there is no $\displaystyle \bold{0} $ vector?