Show that: a if q is positive definite, then the diagonal elements are positive. b let q be a symmetric matrix. if there exist positive and negative elements in the diagonal, then q is indefinite.
a. If q is positive definite, then the diagonal elements are positive.
b. If q is positive definite, then the off-diagonal elements are non-negative.
c. If q is positive definite, then the determinant of q is positive.
d. If q is positive definite, then the eigenvalues of q are all positive.