(a) Prove that a positive definite matrix has positive determinant: det K > 0. (b) Show that...

Question:

(a) Prove that a positive definite matrix has positive determinant: det K > 0.
(b) Show that a positive definite matrix has positive trace: tr K >0.
(c) Show that every 2 x 2 symmetric matrix with positive determinant and positive trace is positive definite.
(d) Find a symmetric 3 x 3 matrix with positive determinant and positive trace that is not positive definite.