I have a matrix A consisting of equations

1 X1 X1^2 X1^3 ...... X1^m

1 X2 X2^2 X2^3 ...... X2^m

1 ...

1 ...

1 Xn Xn^2 Xn^3 ...... Xn^m

I must show that the collumns of A are linearly independantif n > mand at least m + 1 of the numbers X1, X2, X3 ... Xn are distinct.

I am having trouble creating an algebraic proof for this, can anyone offer any insight?

thanks very much