Which of the following sets (with natural addition and multiplication by a scalar) are vector spaces. Justify your answer. a) The set of all continuous functions on the interval [0, 1];
b) The set of all non-negative functions on the interval [0, 1];
c) The set of all polynomials of degree exactly n;
d) The set of all symmetric n × n matrices, i. e. the set of matrices A = {aj, k}n j, k=1 such that A^T = A.