Question

what is the degree of the detrminant |a b|
|c d|​

Answer 1

Answer:

By the basic property of a determinant, that it is 0 if two of its rows are the same, we can deduce that determinant of a VanderMonde matrix will be 0 when any two of its rows are the same. But that means that, as a polynomial, it must have (xi - xj) as a factor, for every i and j.