Find the Jacobian of the transformation x = u, y = 2v, z = 3w.
A)1
B)2
C)3
D)6
E)-1
F)-2
G)-3
H)-6

Name: Find the Jacobian of the transformation x = u, y = 2v, z = 3w. A)1 B)2 C)3 D)6 E)-1 F)-2 G)-3 H)-6
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Question

Quizplus · Accepted Answer

The Jacobian of the transformation is the determinant of the matrix of partial derivatives. We have:

| 1  0  0 |
| 0  2  0 |
| 0  0  3 |

The determinant of this matrix is 1 x 2 x 3 = 6, so the answer is D, 6.

Find the Jacobian of the Transformation X = U, Y