(a) Suppose that A has characteristic polynomial p(A) = X³(2+A)*(A– 3)*. In a table, list the eigenvalues of A, along with their algebraic multiplicities. Using this, find the order of A. |(b) If A has a ten-dimensional column space, what is the nullity of A? Is A diagonal- izable? Explain.

Find the characteristic polynomial and the eigenvalues of the matrix. 5 [14] 7 The characteristic polynomial is (Type an expression using as the variable. Type an exact answer, using radicals as needed.)

Calculate the characteristic polynomial of the following matrix A, and use it to compute the eigenvalues of A. -8 4 A = 14 4 6 -2 4 -6 How to enter polynomials: something like 2- 3*r + 4*r^2 - 5*rA3. Remember to use * for multiplication! Enter the characteristic polynomial of the matrix A: Note: Use r as the polynomial variable. Enter the eigenvalues of A separating them by commas: something like 1, -2, 5.

Let A = = -8 2 2 2 2 -5 4 4 (1) Compute the characteristic polynomial of the matrix A. (2) Find the eigenvalue of A and their multiplicities. (3) Is A invertible? Why?