(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The pair of variables (x, y) are each functions of the pair of variables (u, v) and vice versa.

Consider the Jacobians A=d(x,y)/d(u,v) and B=d(u,v)/d(x,y). Show using the chain rule that the product AB of these two matrices equals the unit matrix I.

2. Relevant equations

3. The attempt at a solution

I wrote out the two Jacobians and tried to multiply them but I got the following:

(dx/du)(du/dx)+(dx/dv)(dv/dx) (dx/du)(du/dy)+(dx/dv)(dv/dy)

(dy/du)(du/dx)+(dy/dv)(dv/dx) (dy/du)(du/dy)+(dy/dv)(dv/dy)

= 2 2dy/dx

2dy/dx 2

Where did I go wrong/ how do I continue this question?

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# Homework Help: Product of Jacobians Proof

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