Find the Jacobian if u = 2xy and v = 2x + 6.
E) u + v

Question

Quizplus · Accepted Answer

The Jacobian matrix for the transformation is:

J =  \begin{bmatrix} \frac{\partial u}{\partial x} & \frac{\partial u}{\partial y}\ \frac{\partial v}{\partial x} & \frac{\partial v}{\partial y} \end{bmatrix}

= \begin{bmatrix} 2y & 2x\ 2 & 0 \end{bmatrix}

Thus, the determinant of the Jacobian is:

det(J) = (2y)(0) - (2x)(2) = -4x

At any point where x is not zero, the Jacobian is nonzero, so the transformation is invertible by the inverse function theorem.

Therefore, the correct answer is D, 11ead0bc_8d9b_ac36_99a0_6b914af1a087_TB6988_11.

Find the Jacobian If U = 2xy and V =