Hi,

I'm trying to show that the following matrix:

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:

is NOT positive definite. I can't find a vector x that showsx^T*B*x> 0.

Thanks a lot for your help.