(a) Generate a 13 times 13 matrix in MATLAB using A = hilb(13). (b) Generate a vector x = [1: 13]. (c) Generate a vector b, where b = Ax. (d) Using only these values of b and A, pretend that you don't know the true value of X. Instead, calculate a value of x by solving the problem x = A^-1 b using an appropriate numerical technique: let's call this value X^cap. (e) Make a plot of X^cap. How large is the residual error of your calculated value, ||b - AX^cap||/||X||? How similar is X^cap to the true value of X, ||X^cap - X||/||X||? (f) Repeat steps (d) and (e) using an inappropriate numerical technique. How does this impact your value of X^cap? (g) Explain why the consistency of the left and right hand sides of the equation AX^cap = b doesn't necessarily mean that X^cap is correct for this matrix A