Enter the following matrices into Matlab -4 A= 2 -1 0 1 0 3 0 -5 -4 5 -2 3 1 -1 -6 2 0 -4 -2 2 -1 0 1 0 1 5 -3 2 3 = (1). Use the rref command on A - XI to check whether 1 = 3 is an eigenvalue of A. (2). Use the Matlab command c=poly(A) to find the characteristic polynomial of A and store it in c. The result tells us the coefficients of the powers of in descending order. Using the coefficients to write out this polynomial in terms of . (3). Use the command polyval to determine the value of the characteristic polynomial at 1 = 5. Use the answer to decide whether 5 is an eigenvalue. (Note: in the command window, type in help polyval to see how to use this command.) (4). Use the command polyval to find the value of the characteristic polynomial at 1 = 0. How would you interpret this answer? Use det to find the determinant of A. What can you say about the two results? Justify your answer. (5). Use the roots command on the characteristic polynomial of A to find the eigenvalues of A. How would you check your answer using the matrix A? (6). Use the Matlab command (V,D] = eig(A) to find the eigenvalues and corresponding eigenvectors of A. This will display two matrices. What do the columns of V repre- sent? What do the diagonal entries of D represent? Is there any correlation between the order of the columns of V and the order of the diagonal entries of D? Justify your answer. (7). Solve the vector equation VX = b, where V is the matrix in (6) and store your solution in f. (8). Evaluate Akb and VD'f for k = 1, 2,5, 8. Explain your observation and justify your