Question

Find the Jacobian of the transformation.
x = 7v + 7w^2
y = 9w + 9u^2
z = 2u + 2v^2

∂(x, y, z)/∂(u, v, w) ??

Answer 1

not a valid transformation, zeros on diagonal
check with
http://www.wolframalpha.com/widgets/view.jsp?id=d6a52679e750c30e320a7094ec975598

Answer 2

well, just plug them in

∂x/∂u = 0
∂x/∂v = 7
∂x/∂w = 14w

∂y/∂u = 18u
∂y/∂v = 0
∂y/∂w = 9

∂z/∂u = 2
∂z/∂v = 4v
∂z/∂w = 0

So J =
(0 7 14w)
(18u 0 9)
(2 4v 0)

|J| = 1008uvw + 126