Consider the matrix A = 1 2 6

2 3 0

6 0 5

1. Compute the Characteristic Polynomial of A, and the Eigenvalues and Eigenvectors of A

2. Using the Eigenvalues and Eigenvectors of A, find an orthonormal matrix P and a diagonal matrix D such that A = P DP 1 .

3. Is the matrix A invertible? If yes, provide an expression of its inverse A1 in terms of P and D, and provide also the eigenvalues of A1

. 4. Use R, Matlab or Python to verify your results from questions 1, 2 and 3