Please solve all questions.

Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix A = 1 1) a) The characteristic polynomial is p(r) = det(A - TI) = b) List all the eigenvalues of A separated by semicolons. c) For each of the eigenvalues that you have found in (b) (in increasing order) 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 is only one eigenvalue, enter the zero vector as an answer for the second eigenvalue. i) Give a basis of eigenvectors associated to the smallest eigenvalue.ii) If there is another eigenvalue, give a basis of eigenvectors associated to this eigenvalue. Otherwise, write the null vector