So the matrix is this:

[ 1 1 1 1 ]

[ a b c d ]

[ a^2 b^2 c^2 d^2 ]

[ a^3 b^3 c^3 d^3 ]

The method I was using was to multiple row 2, 3, 4 by 1/a, 1/a^2, 1/a^3, then subtract from row 1. Then multiply row 3 and 4 such that I can subtract from row 2, etc.

The problem with this method is that I'm getting a lot of computation and i'm starting to wonder if i'm do this the right way. Is there a better way of doing this?