I'm having trouble understanding where this concept comes from: Step 1) If you start out with the following two equations v + log u = xy u + log v = x - y. Step 2) And then perform implicit differentiation, taking v and u to be dependent upon both x and y: (d will represent the partial derivative symbol): dv/dx + (1/u)du/dx = y du/dx + (1/v)dv/dx = 1 I can do some simple Gaussian reduction and obtain: du/dx = [u(v-y)]/[uv-1] which is the same answer my book gives, the only difference is that my book uses this method to find du/dx: Step 3) det(Row 1:yu, u; Row 2: v, 1)/det(Row 1: 1, u; Row 2: v, 1) which reduces to: (yu)(1) - (u)(v))/(1)(1) - (u)(v). If the two matrices were A, and B, respectively, then: a11 = yu, a12 = u, a21 = v, a22 = 1. b11 = 1, b12 = u, b21 = v, b22 = 1 (sorry, I don't know how to put a real matrix into here) And my problem is that I just don't understand where these matrices came from. I think this may be some formula from linear algebra that I just don't remember, but my book gives no reference to what it's doing, and goes directly from step 2 to step 3, so I'm really kind of lost right now. Any help would be appreciated.