19. Let C be defined by *c*_*ij* = *a*_*ij**b*_*ij*, *i, j* = 1, 2, 3, where A and B are positive definite matrices defined below. Show that C is positive definite, and hence illustrates Theorem 12.2.8.

A =

[ 3 1 -1 ]

[ -1 2 2 ]

[ -1 2 4 ]

B =

[ 1 -1 1 ]

[ -1 4 1 ]

[ 1 1 6 ]