Thread: Determinant with Exponents

I was working on a problem, I need to show that a certain type of equation has a unique solution. By Cramer's Rule the problem reduces to:

I asked my teacher he said there is a name for it, but did not know much about it. Someone know what this is? Or how to prove it?

Vandermonde Determinant

Thank you really helps. Now I can complete the proof.

You should have caught my mistake, it must have been,

Because otherwise it is non-square.
---------
Can you demonstrate that for the regular Vandermonde Matrix

A proof can be found here.