Do the following using Matlab: Let A be the following matrix, given in Matlab format: A = [1 8 -1 8 1; 0 1 8 -1 8; 0 0 1 8 -1; 4 1 4 1 4; 7 8 2 6 2] Find the eigenvalues of A in two ways:

(a) First use the Matlab eig function to find the eigenvalues directly.

(b) Second, use the Matlab poly function to find the characteristic polynomial. Then use the Matlab roots function to find the roots of that polynomial. (Look up, in the Matlab documentation, how to use these functions; their use in this problem is not complicated.)

(c) Are the results exactly the same? Almost the same? Not at all the same?

For this problem, turn in a diary or script showing both the Matlabs statements used, and Matlabs output for parts (a) and (b). Then add your answer for part (c) as a text insertion into your Matlab answer file.