Linear Algebra Help

[TVG]

I am trying to determine the definiteness of a couple quadratic forms.

In the first question, I was able to turn it into a matrix, and do my usual calculations by using the Aij = Aji = (Aij + Aji)/2 formula.

The second question doesn't have all the terms to be able to do that. I am missing 4 numbers in the matrix. Are these just zeros?

Here is the question. The x, y, z are (X sub 1), (X sub 2), (X sub 3) respectably.

q = 2x^2 - 3y + 5z^2 -8xz

The only matrix I can get out of that is

2 , # , -4
# , -3, #
-4, # , 5

[TVG]

Found out answer from prof. The missing terms are just 0's.