#4. (a) (15 points) Let f(x, y) = (x] +y', x + y). Compute [Df(2, 1)], Ar(2, 1) and [Df (2, 1) ]-1. Show that an inverse function f- exists and is C' from some open set W containing (5, 3) onto some open set V containing (2, 1). Find the Jacobian matrix [D(f-) (5, 3)] for this inverse function f-1. (b) (15 points) Prove that there exist C' functions u = u(x, y) and v = v(r, y) defined in some open set V in R- containing the point (1, 1) such that u(1, 1) = 1, v(1, 1) =1, and