2. (25 pts.) Consider the following matrix: 4 0 1 0 041 0 1 1 42 0 2 4 (a) Find the characteristic polynomial of the matrix by performing the co-factor expansion of the determinant of A - XI. (b) Find the eigenvalues, either by hand, or using MATLAB's roots command. (c) By hand, or using the interactive MATLAB technique demonstrated in class, find the eigenvectors. (d) Use MATLAB or other software system to demonstrate that the eigenvectors form an orthonormal set of vectors. (e) Compute the Rayleigh Quotient to demonstrate your solution is cor- rect.