Problem 4. Take m = 50, n = 12. Using MATLAB's linspace, define t to be the m-vector corre- sponding to linearly spaced grid points from 0 to 1. Using MATLAB's vander and fliplr, define A to be the m x n matrix associated with least squares fitting on this grid by a polynomial of order n - 1. Take b to be the function cos(4t) evaluated on the grid. Now, calculate and print (to 16 digit precision) the least squares coefficient vector x by the following three methods. (a) Solving the normal equation explicitly computing (AT A)-1. (b) Using the MATLAB implementation of the classical Gram-Schmidt algorithm cgs. (c) QR factorization using MATLAB's qr, which is based on the Householder triangularization. (d) x = A \\ b in MATLAB, which is also based on QR factorization. (e) The calculations above will produce five lists of twelve coefficients. In each list, shade with red pen (or highlighter/marker) the digits appear to be wrong (affected by rounding error). Comment on what differences you observe. Do the normal equations exhibit instability? You do not have to explain your observations