Given the transformation u=x+yu = x + yu=x+y and v=x−yv = x - yv=x−y, what is the Jacobian ∂(x,y)∂(u,v)\frac{\partial(x, y)}{\partial(u, v)}∂(u,v)∂(x,y)?
−1-1−1
111
−12-\frac{1}{2}−21
12\frac{1}{2}21