Final answer:
The Jacobian of the given transformation x = 3uv, y = 4vw, z = 6wu is a matrix formed by taking the partial derivatives with respect to u, v, and w. In this case, the Jacobian matrix is | 3v 3u 6w |.
Step-by-step explanation:
The Jacobian of a transformation is a matrix of first-order partial derivatives used to calculate changes in variables when transforming between coordinate systems. To find the Jacobian of the given transformation x = 3uv, y = 4vw, z = 6wu, we need to find the partial derivatives with respect to u, v, and w. The Jacobian matrix is then formed by taking these partial derivatives and arranging them as rows or columns. In this case, the Jacobian matrix would be:
| 3v 3u 6w |