Question

(iii) What is the degree of the determinant
(A) 1 (B) 3 (C) 4 (D) 2
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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.