Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix -1 0 0 A=0 -10 -3 -3 2 a) The characteristic polynomial is p(r) = det(A-rI) = b) List all the eigenvalues of A separated by semicolons. BM c) For each of the eigenvalues that you have found in (b) (working from smallest to largest) give a basis of eigenvectors. If there is more than one vector in the basis for an eigenvalue, write them side by side in a matrix. If there are fewer than three eigenvalues, enter the zero vector in the unneeded answer fields below. i) Give a basis of eigenvectors associate to the smallest eigenvalue. ab sin (a) f α Ω дх B ii) If there is a second eigenvalue (the second-smallest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. ab sin (a) f dx 8 Ω P iii) If there is a third eigenvalue (the largest), give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector. a sin (a) дх f ४ Οι Ω Az P