4. true or false. for all subquestions below assume that a is an m × n real matrix and s is an n × n symmetric matrix (a) t f all eigenvalues of at a are non-negative. (b) t f at a and aat have same set of eigenvalues if not counting the repeated zeros. (c) t f: if a has only positive singular values then the nullspace of a is an empty set. (d) t f let rx) -, x r", then for any real mumber k; r(kx) > r(x). (e) t f: let d be an n × n real diagonal matrix, then the maximum and minimum values of r(x) ? , x e r", are the largest and smallest diagonal entries of d.