Using Matlab:

6. HOMEWORK #8 If a matrix A has dimension nxn and has n linearly independent eigenvectors, it is diagonalizable. This means there exists a matrix P such that P-1AP D, where D is a diagonal matrix, and the diagonal is made up of the eigenvalues of A. P is constructed by taking the eigenvectors of A and using them as the columns of P. Your task is to write a program (function) that does the following . Finds the eigenvectors of an input matrix A Checks if the eigenvectors are linearly independent (think determinant) - if they are not linearly depended, exit the program &display error . Displays P, P1 and D (if possible) Shows that PDP-1 A Show that your program works with a 3x3 matrix A