Econ 407: An example for computing eignevalues for a 3 by 3 matrix and demonstrating that the

product of the eigenvalues is the same as the determinat of the matrix. Use the following B matrix

and find the determinant, and eigenvalues.

> B:=matrix([[4,0,1],[-2,1,0],[-2.0,0,1]]);

> detb:=det(B);

> B1:=matrix([[4-lambda,0,1],[-2,1-lambda,0],[-2.0,0,1-lambda]]);

> with(linalg):

Warning, new definition for norm

Warning, new definition for trace

> detb1:=det(B1);

> solve(detb1,lambda);

The three roots are 1, 2, and 3. If you multiply these roots you get 1*2*3=6. QED.