2. Define g: R’ – R’ by g(x, y, u, v) = ( xy ty’ – uv, x? + 2xy – u’ + v? ).

(a) (1 point) Is the Jacobian of g a 2 x 4 matrix?

O Yes

O No

(b) (2 points) Compute the Jacobian of g.

(c) (3 points) Use the Jacobian of g to approximate

g(x + Ar, y + Ay, u + Au, v + Av) – g(x, y, u, v)

for (x, y, u, v) = (1, 1, 2, 1) and Ax = Ay = Au = Av = 10-3.Math