(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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Product of Jacobians Proof

**Physics Forums | Science Articles, Homework Help, Discussion**