Originally Posted by

**AKTilted** Hi,

I'm trying to show that the following matrix:

$\displaystyle A = \begin{bmatrix} 1&2&3\\2&5&1\\3&1&36 \end{bmatrix}$ is positive definite. Using the typical definitions I get to this inequality:

x^2 + 2x*(2y+3z) + 5y^2 + 2*y*z + 36z^2 > 0. I just don't know to show that this is true.

Also, I'm trying to show that this matrix:

$\displaystyle B = \begin{bmatrix} 1&2&3\\2&5&1\\3&1&34 \end{bmatrix}$ is NOT positive definite. I can't find a vector x that shows **x**^T*B***x** > 0.

Thanks a lot for your help.