MATLAB *This is my matlab homework from Linear algebra course. Please provide me with the matlab codes! thank you :) *

15-115 25] 5. Let A= | 2-18 60 17 a) Execute the command [P,D]eig(A) to diagonalize A (b) Use MATLAB to verify that A PDP-1 (c) Use the previous results to give the eigenvalues of A, and give an eigenvector for each eigenvalue. (d) MATLAB produces eigenvectors in such a way that they have length 1. A consequence is that the entries look a little messy. The eigenvectors in this example can all be rescaled so that their entries are all single digit integers. Do this rescaling to give nicer looking eigenvectors. (Hint: try multiplying each vector by its largest denominator and then divide by the smallest thing you see.) (e) Enter your rescaled eigenvectors as the columns of a matrix Q. Then verify that A = QDQ-1. (Any basis of eigenvectors can be used to diagonalize a matrix.)