For an m ( n matrix A, let the set of all vectors x in Rn such

Question:

For an m ( n matrix A, let the set of all vectors x in Rn such that Ax = 0 be denoted by NS(A), which in Example 10 of Section 4.3 has been shown to be a subspace of Rn, called the null space of A.
(a) Prove that rank A + dim NS(A) = n.
(b) For m = n, prove that A is nonsingular if and only if dimNS(A) = 0.