Find Eigenvalues without function "eig"

I performed this by hand and know that the eigenvalues are 10, -1, and 4. But clearly that's not what I got... Any help would be nice.

[Bruno Luong]

correct value of x2 is 13 (not 7)

Answer 1

[KSSV]

syms x
A = [10 0 0; 1 -3 -7 ; 0 2 6] ; 
p = det(A-eye(3)*x)   % this is the characteristic equation 
val = solve(p)        % solve this for roots 

The polynomial equation, you get is:

poly =

Using roots:

p = [-1 13 -26 -40] ;
val = roots(p)

Answer 2

[Paul]

roots(poly(A))

Though I’m sure one could come with an A for which this approach will fail due to numerical accuracy issues. In which case converting A to a syms object as in another answer may be preferred.