Answer: Show that the normal equations (8.3) resulting from discrete least squares
Chapter 8, Problem 14(choose chapter or problem)
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. [Hint: Let A = (aij), where aij = m k=1 x i+j2 k and x1, x2, ... , xm are distinct with n < m 1. Suppose A is singular and that c = 0 is such that ct Ac = 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.]
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