5. Given data points as follows: where i is the weighting factor to represent the reliability of the i-th data point. Use least-squares method to best fit these data points by the form of f(x)=c0+c1x+c2x2 (a) Derive the normal equations (including the weighting factors). (5 pts) (b) Use the normal equations developed in part (a) and the Gauss-Jordan direct method to compute the solution (digits aligned with given data through rounding step-by-step for the coefficients: c0,c1, and c2; and the deviation E(c0 pt) 2/3 (c) Use the normal equations developed in part (a) and the Gauss-Seidal indirect method to write a MATLAB code to compute coefficients: c0,c1, and c2; and the 2 deviation E(c0,c1,c2). Three iterations only and the initial guesses for c0,c1, and c2 are all zeros. ( 10pts) (d) Follow your computer program developed in part (c), use hand calculations to check your computational results. Also compare your computation results with those obtained in part (b). (5 pts) c0c1c2=1.740.0630.501f(xi)=1.74+0.063x1+0.501x2E(c0,c1,c2)=i=03wi[f(xi)yi]2=4.176103