Solution to T7 in 4.4.

> with(linalg):

Warning, the protected names norm and trace have been redefined and unprotected

> A:=matrix([[1,1,2,1,1],[1,2,3,2,1],[2,3,1,2,1],[1,2,2,3,1],[1,1,1,1,7]]);

> I5:=Matrix(5,5,shape=identity);

> det(A-x*I5);

> plot(-31+121*x-59*x^2-39*x^3+14*x^4-x^5,x=-2..10,y=-200..200);

After using several graphing windows, I can now see all five roots. They are, approximately: -1.9, 0.35, 1.06, 5.26, and 9.25.

We could use Newton's Method to improve the accuracy if needed.

> eigenvalues(A);

Conclusion: Maple was unable to factor the characteristic polynomial. However, we apply the evalf command to convert this to floating point numbers. (See HELP evalf for details.)

> evalf(%);

>