An n x n symmetric matrix A is positive semi definite if xT Ax 0 for

Question:

An n x n symmetric matrix A is positive semi definite if xT Ax ≥ 0 for all x in Rn. Prove the following:
(a) Every positive definite matrix is positive semi definite.
(b) If A is singular and positive semi definite, then A is not positive definite.
(c) A diagonal matrix A is positive semi definite if and only if an ≥ 0 for i = 1, 2,.... n.