Probably not able to get the partial derivatives of the function right...

Ok, first off, have a Force that is a function of position: F = ax, where a is a constant--I know the solution to the curl is a in the direction of z; not conservative. But, when I set up my cross product matrix I have for the partials in the z and z direction as zero, and the Fy and Fz too. Now this leaves me with only a and ax in the i column of my matrix-- that gives zero, so I'm doing something wrong.

Second I have a Force function that I know is conservative:

F = (yz^2)i + (xz^2 + 2)j + (2xyz -1)k

when I take the partials of the function I get,

Fx = z^2 + 2y

Fy = Z^2 + 2xy

Fz = 2yz + 2xz +2xy

Now, when I place these partials in the top row and place the Function components in the bottom row-- I do not get a zero cross product.

Please tell me what I'm doing wrong.

Thanks