2) Consider the Hilbert matrix, A, whose elements are given by i+j-1 Write a script m-file to do parts (a)-(e) below. You will use the function norm(x) for the norm (which is the 2-norm), cond(A) for the condition number (which is the 2-norm condition number), and the relatively stable backslash "command to solve a linear system. Use MATLAB to do all the following computations: Page 3 of 4 a) Use nested loops to compute the matrix, A, for any You do not need to use loops for the remaining parts of the problem b) Let the exact solution to some problem, Ar-, be x = ones (n,l). For n = 10, use MATLAB to find b . Now, compute the solution x( of Ax = b using the backslash"\", command Use your results from part (b) to help compute the following: c) Compute the relative backward eror d) Compute an upper bound for the relative forward error if the exact solution were not known. e) Compute the relative forward error f) According to our discussion in class, at most how many digits can be trusted in your solution for n- 10 if the exact solution were not known