Coordinate Transform Problem

[manny]

Hello,

 

I'm taking Wave Propagation Through Solids and I am required to have a background in linear elasticity. Unfortunately, I haven't take that course.

 

Knowing that the coordinates x₁ , x₂ , and x₃ of a point are three independent variables, how can I show that the relation A_i = (dx_j/dx_i)A_j implies A_i = (dx_j/dx_i)A_j

Where A and x denote the transformed coordinates?

 

I'm thinking I might have to use the Kronecker Delta or transform differentials..but I'm not sure how to prove this.

 

Any help? Thanks!