I am slowly but surely trying to learn Matlab so any extra notes in the code would be very appreciated!

(3) (The Hilbert Matrix) The description of this problem uses MATLAB commands. If you are using another language, you should find a package that has commands to solve a linear system by LU decomposition and compute the condition number of a matrix ask me if you need help). You might need to write your own code to generate the Hilbert matrix and the right hand side b. The infamous n x n Hilbert matrix H, has entries H ij) = 1/(i+j-1). For a specific value of n, we define the right hand side vector bn by having entries equal to the row sums of the Hilbert matrix. For example: 1 1/2 bs H2 = 1.5 1/2 1/3 B2 = 0.83333 Use the MATLAB commands Hn - hilb(n); bn - sum (Hn'); to generate the Hilbert matrix Hn and a right-hand side bn. It should be clear that the true solution to the system Hnx = bn is the n-dimensional vector in = (1,1,..., 1)". Use the MATLAB commands [Ln, Un] = lu(Hn) xn - Un\(Ln\bn) to solve this linear system for n = 5, 10, 15, 20. For each n, provide the calculated solution vector in. Then, compute the relative error and the relative residual using the norm || lloc Report these errors and residuals in table form. Discuss the results of these experiments, and propose an explanation. The MATLAB command cond may be helpful