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 independant if n > m and 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