The Vandermonde determinant is the determinant of an n x n matrix of the following form: 1 n-1 2 1 In . . . in-1 n The determinant turns out to be equal to ITlizjzn(*j -xi), for any num- bers x1, . .. ,Cn. The purpose of this problem is to verify some special cases.(a) For which values of x does the following matrix A have determinant zero? 1 A = 1 2 4 (b) Verify the formula by direct computations when n = 2. That is T1 det = 12 - $1 . 1 (c) Verify the formula by direct computations when n = 3. That is 1 X1 det 1 12 = (X2 - x1)(x3 -X2) (23 - 21). rot 1 X3