8.11 Solving normal equations versus QR factorization. In this problem we compare the accuracy of the two methods for solving a least squares problem minimize || Ax 6||2. We take [ 1 10-k 1 0 10-k ] , [ -10-k 1 1+ 10-k A= b= 1-10-k for k= 6, k = 7 and k = 8. (a) Write the normal equations, and solve them analytically (i.e., on paper, without using MATLAB). (b) Solve the least squares problem in MATLAB, for k = 6, k = 7 and k = 8, using the recommended method x = A b. This method is based on the QR factorization. (c) Repeat part (b), using x = (A*A) I (A*b). Compare the results of this method with the results of parts (a) and (b). Remark. Type format long to make MATLAB display more than five digits