# Math Help - How to find the eigenvalues of a 3x3 matrix

1. ## How to find the eigenvalues of a 3x3 matrix

[1 1 1]
[1 1 1]
[1 1 1]

1) why can't i just do guassian elimination to make it
[1 1 1]
[0 0 0]
[0 0 0] then the eigenvalues would be 1, 0

2) if i just do it straight i get
[1-λ 1 1]
[1 1-λ 1]
[1 1 1-λ] and then i get

(1-λ)( (1-λ)(1-λ) - 1 ) - (1)( (1)(1-λ)-1 ) + (1)(1-(1-λ))

and it simplifies to -2 + λ + 3λ^2 - λ^3

how do i get the eigenvalues from here?

thanks

2. Originally Posted by cnix
then the eigenvalues would be 1, 0
Due to the paricular form of the matrix, one can see that

$\begin{pmatrix}1&1&1\\1&1&1\\1&1&1\\\end{pmatrix}\ begin{pmatrix}1\\1\\1\\\end{pmatrix}=3\begin{pmatr ix}1\\1\\1\\\end{pmatrix}$

and it simplifies to -2 + λ + 3λ^2 - λ^3
That's wrong. The roots of the polynomial you will find are the eigenvalues.