Show that the normal equations (8.6) have a unique solution. [Show that the only solution for the

Question:

Show that the normal equations (8.6) have a unique solution. [Show that the only solution for the function f (x) ≡ 0 is aj = 0, j = 0, 1. . . n. Multiply Eq. (8.6) by aj , and sum over all j. Interchange the integral sign and the summation sign to obtain

Thus, P(x) ≡ 0, so aj = 0, for j = 0. . . n. Hence, the coefficient matrix is nonsingular, and there is a unique solution to Eq. (8.6).]