Help with d, e, and f

Although it appears in various applications, the Hilbert matrix is notoriously ill-conditioned. Generate a single precision 6 times 6 Hilbert matrix (H) using the hill command. Find the condition number of the matrix. Define a single precision vector, b, of length 6 which has each element equal to 1. You may use the ones command to do this. Find H^-1, the inverse of H. Find a solution to Hx_H = b by multiplying the inverse of H by the vector b. Estimate the error (e) in the solution using the expression e = H^-1r. The true solution is x_t = [-6, 210, -1680, 5040, -6300, 2772]^T. Find the true error, e_t. Explain why this value is not the same as the error calculated in part (c). Does the expression given in class, ||e||/||x_T|| lessthanorequalto condo (A)||Delta A||/||A|| reasonably predict the expected number of significant (correct) digits in the calculated solution? Explain and show your work. Find a solution to Hx_H = b using the left divide function and find the true error. Compare this result with that in part d. What conclusions can you draw regarding the accuracy of using different methods of solving linear systems in MATLAB? Although it appears in various applications, the Hilbert matrix is notoriously ill-conditioned. Generate a single precision 6 times 6 Hilbert matrix (H) using the hill command. Find the condition number of the matrix. Define a single precision vector, b, of length 6 which has each element equal to 1. You may use the ones command to do this. Find H^-1, the inverse of H. Find a solution to Hx_H = b by multiplying the inverse of H by the vector b. Estimate the error (e) in the solution using the expression e = H^-1r. The true solution is x_t = [-6, 210, -1680, 5040, -6300, 2772]^T. Find the true error, e_t. Explain why this value is not the same as the error calculated in part (c). Does the expression given in class, ||e||/||x_T|| lessthanorequalto condo (A)||Delta A||/||A|| reasonably predict the expected number of significant (correct) digits in the calculated solution? Explain and show your work. Find a solution to Hx_H = b using the left divide function and find the true error. Compare this result with that in part d. What conclusions can you draw regarding the accuracy of using different methods of solving linear systems in MATLAB