Show that the normal equations (8.3) resulting from discrete least squares approximation yield a symmetric and nonsingular matrix and hence have a unique solution. [Let A = (aij), where


and x1, x2, . . . , xm are distinct with n < m − 1. Suppose A is singular and that c ≠ 0 is such that ctAc = 0. Show that the nth-degree polynomial whose coefficients are the coordinates of c has more than n roots, and use this to establish a contradiction.]