You already know that one eigenvalue is -2.
Now, instead of factoring the polynomial, you can use these two facts to find the remaining two:
I need to determine eigen values for the following matrix.
- 3 2 -1
2 2 -6
-1 -6 5
I get Det of A - lambda I =
I will use x instead of lambda
(-3 - x) (2 - x) (5 - x) - 36(-3 - x) - 4 (2 - x) + 10 + x = 0
I know my factoring skills need work, but is there another way besides trial and error to determine my eigenvalues??? I get that lambda (or x as I have used) = -2 is one of my eigen values. I also understand, I think, that I should have two more. Is there a method I am not aware of or a site on the internet that has a tutorial for this process. So far all the ones I have found just use 2 x 2 matrices which are so simple even I can do them!!! Thanks so much for looking at this. Frostking