Assignment N0. 4 MSDA 3045 Mathematical Statistics Each question carries 10 marks each and provide the Python code for questions 1. Question 1 Compute (a) the characteristic polynomial of A, (h) the eigenvalues of A, (c) the eigenvectors of A. 4 0 l A: 2 3 2 1 0 2 Question 2 (a) Show that, for any square matrix A, AT and A have the same characteristic polynomial and hence the same eigenvalues. (b) Give an example of a 2 X 2 matrix A for which AT and A have different eigenspaees(eigenveetors). Question 3 Let A and B be n X n matrices with eigenvalues A and M, respectively. Give an example to show that A + n need not be an eigenvalue of A + B. Question 4 Show that if A is invertible with eigenvalue /\\ and corresponding eigenvector X, then % is an eigenvalue of A'1 with corresponding eigenvector X