calc_tutorial_15_6_013

 
Problem Statement

{3,5,7}
{2,4,6}
{3,4,5}
5*(-4)-6

Compute the Jacobian.

G(u, v) = (5u + 6v, u − 4v)

 
Step 1

Question Sequence

Question 1

Recall the definition of the Jacobian.

The Jacobian of a map G(u, v) = (x(u, v), y(u, v)) is the following determinant.

Jac(G) = ∂(x, y) / ∂(u, v) = the determinant of the following table interpreted as a matrix.

(∂x / ∂u) (∂x / ∂v)
(∂y / ∂u) (∂y / ∂v)
Table : Matrix A

Jac(G) = ∂(x, y) / ∂(u, v) = det(Matrix A) = (∂x / ∂u)(∂y / ∂v) - (∂x / ∂v)(∂y / ∂u)

For x(u, v) = 5u + 6v, and y(u, v) = u − 4v, calculate the partial derivatives in the Jacobian.

(∂x / ∂u) =

(∂x / ∂v) =

(∂y / ∂u) =

(∂y / ∂v) =

Correct.
Incorrect.

 
Step 2

Question Sequence

Question 2

Compute the Jacobian.

∂(x, y) / ∂(u, v) = (∂x / ∂u)(∂y / ∂v) - (∂x / ∂v)(∂y / ∂u) =

Correct.
Incorrect.