$6.(6\mathrm{.}3\mathrm{.}35)$ A positive definite matrix cannot have a zero $($or even worse, a negative number$)$ on

its main diagonal. Show that this matrix fails the energy test xTSx $>0$:

$$

$$

$411$

$102$

$125$

$$

$$

$$

$$

x$1$

x$2$

x$3$

$$

$$

is not positive when $($x$1,$ x$2,$ x$3)=(,,).$