How do I solve a Jacobian problem involving a determinant?

[Centurion1]

Not sure if this is where I should put this but currently I am taking math for econ and we are on special determinants (jacobian, Hessian, Bordered Hessian, some Leontiff)

So I have this problem in my notes that I am basically basing my exam studying around since the book isn't the best. It is a Jacobian heading into a hessian but I am more confused about the Jacobian. So this is what I have

z = 2x² + 4y² - 2xy + 65 + λ(32-x-y)

z_x = 4x - 2y + λ
z_y = 8y - 2x +λ
z_λ = 32-x-y

Then it goes into the matrice and I have written

4 -2 -1 x 0
-2 -8 -1 y = 0
-1 -1 0 λ -32

lJl = lAl = -16 ≠ 0 p(a) = 3

Ok so once I have made the matrice (which makes sense to me) I can even find the determinants of the first part. I am just confused how 0 0 -32 came about and also where the last bit which i assume is the final answer means. I can do a 2x2 Jacobian easily its when it is like this that confuses me. What step am I missing. Also if this is the wrong section I apologize feel free to move it. I just googled how to do something and this was where something on determinants was

 

[Centurion1]

Im sorry I just realized that this should be in Homework help. If a moderator would move it please. I am sorry for cluttering yalls forum.