Hey guys.
Im having a problem with deciphering positive definite and negative definite for this quadratic form i determined from a matrix.
I dont quite understand how to evaluate if its pos def or neg def.
From what I see in my notes, q(x,y) > 0 for all x not equal to 0. This doesnt help much as with some terms being squared and some not, im not sure if q will always be positive. I also dont know if there is anything different being a 3-variable quadratic. Anyways here it is:

q(x, y, z) = 2x - 2xy + y - 8yz 2xz + 5z

Any help is appreciated