Cholesky factorization versus QR factorization. In this probiem we compare the accuracy of the two methods for solving a least-squares problem minimize "As: bll2. We take 1 1 1rr" A: 10* 0 , b: 1+1u-k , 0 10-* 1 10"\" forkz, k=7andk=8. (a) Write the normal equations, and solve them analytically (113., on paper, without using MATLAB). (b) Solve the least-squares problem in MATLAB, for k = 5, k = 7 and k = B, using the recommended method :I: - A\"). This method is based on the QR factorization. (c) Repeat part (b), using the Cholesky factorization method, i.e., x I 01' th)'. (A'b). (We assume that MATLAB recognizes that ATA is symmetric positive denite, and uses the Cholesky factorization to solve ATAzc = ATb). Compare the results of this method with the results of parts {a} and (b). Remark. Type format long to make MATLAB display more than ve digits