Using matlab

-LUll l ms and Diagonalization Using Matlab Poblems 1. Find the eigenvalues and eigenvectors of each of the following matrices using Two different approaches (a) First use the 'long way'. Find the eigen solution by solving the characteristic polynomial given by IA AII 0. Then solve for each eigenvector using the given eigenvalues. You may use Matlab's poly and roots commands as well as rref to help (b) Check your results for (a) by using the eig command. Rescale the eigenvectors Matlab gives you so they look like those you found in part (a) 5 0 0 A 1 0 3 0 0 -2 1 0 0 0 0 4 1 0 0 0 -3 1 0 0 1 -2 2. Consider the following pair of 3 x 3 matrices -4 7 3 8 1 2 3 4 3 -2 1 3 4 7 3 8 1 2 3 4 3 -2 1 3 (a) Which of the matrices is singular? (b) Find the eigenvalues and eigenvectors of each of the matrices. (c) Are the matrices diagonalizable? (d) Construct two singular matrices One 3 x 3 and one 4 x 4) and find their eigenvalues and eigenvectors. What do you notice about the eigenvalues of a singular matrix? (e) For A and B given above, and b solve the nonhomogeneous systems: Ax using diagonalization (ie: Transform coordinates to x Py where P is the matrix of eigenvectors. Check your results using rref