Using Computer Algebra Systems

MATLAB can do matrix operations . We first define two matrices and a vector,A, B, and $\nu$:

>> A = [ 4 1 -2 ; 5 1 3 ; 4 0 -1]
>> B = [ 3 3 1 ; -2 1 5 ; 2 2 0]
>> v = [ -2 3 1] 
>> vt = v'
>> det(A)
>> trace (A)
We can get the characteristic polynomial;
>> poly(A)
ans =
1.000   -4.0000   2.0000   -21.0000
where the coefficients are given. This represents
x^4 - 4x^3 + 2x -21