Chud Easy linear algebra problem

[Apeson]

Let T be the operator on R^3 whose matrix representation is:
(1 −1 0 )
(0 0 0 )
(−2 2 2 )
Then the eigenvalues of the operator T^5 − 3T^4 + T^3 − T^2 + T − 3I are ____ ,____ , and ____ ?

 

[Notta]

use LaTeX, fag

 

[Apeson]

use LaTeX, fag

i wont because i'm a selfish little fuck

 

[Notta]

there must be an easier way to do this instead of solving a quintic, especially with T being a matrix. i am NOT going to do T^5

 

[Apeson]

there must be an easier way to do this instead of solving a quintic, especially with T being a matrix. i am NOT going to do T^5

You VILL solve a quintic and you VILL have fun while doing it or something

 

[Apeson]

Jokes aside, it's been a while since i've done an eigenvalue exercise, but i can tell that an entire row of zeroes on a matrix is worth paying attention to.