43 Vandermonde Determinants. All variables represent real (or complex) numbers. a Show 1 1 1 a b = (b-a)(c-a)(c-b). a b c Hint: The determinant is of small enough order to expand and simplify. This is straightforward, but non-instructive, not to mention uninteresting. Instead, try the following. The determinant is a polynomial P of degree two in c with zeros c = a and c = b. Why? So P(c) = K(c a)(c b) for a constant K to be determined. K is the coefficient of c in P(c). Show K = b a and you're done. 1 1 X1 X2 b. Prove 1 Xn I (x; -x) II -1 1si