Problem 5. The least squares approximation method taught in class is for discrete data. There is a corresponding method for approximating dat.a given as a continuous function. Consider approximating f(x) by a quadratic polynomial on the interval 0 1. Do so by choosing a, a2 and as to minimize the root-mean-square error Derive the linear system satisfied by the optimurn choices of ai, a2, , what is its relation to the Hilbert matrix in Problem 2