Consider the intersection of level surfaces of F = x^3 + y^3 - u^3 - v^3 and G = xu + yv.

(a). Write down the linear equations in matrix form to decide on solving for solving for x and y as functions of u and v near (x0, y0, u0, v0).

(b). Write down the matrix equation for solving for dx/du and dy/du near (x0, y0, u0, v0).

(c). Describe the points (x0, y0, u0, v0) near which you may be unable to solve for x and y as functions of u and v near (x0, y0, u0, v0).