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Compute the Jacobian $J(u, v)$ for the following transformations.

$$T: x=(u+v) / \sqrt{2}, y=(u-v) / \sqrt{2}$$

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I was Just find the country cobian for the given transformation X equals U plus view of square to wise equal to u minus. Fear was heard to So the Jacoby in is gonna be equal to Sorry. Okay. Unequal to partial of ex respect to you is one over the square to partial extractive e is one over the square to two partial y. With respect to you is one over squared to partial wise work to be is negative one over the square to That means that the determinant is going to be negative 1/2 minus a positive 1/2. And that is simply going to be negative one and we are done.