Finding Eigenvalues with the Determinant Method

[cscott]

Homework Statement

I need the eigenvalues and eigenvectors of [[0,0,1][0,2,0][1,0,0]]

The Attempt at a Solution

How come when I use the determinent method to get the eigenvalues I only end up with 2? Did I make a mistake or is there some other way I'm supposed to find -1, +1?

 

[Hurkyl]

If you mean what I think you mean, then you must have made a mistake. Can you show your work?

 

[cscott]

I used the cofactor expansion along the first row, like on wikipedia so the first two terms are zero and then for the last term: (1)det{ [[0, L-2][1, 0]] } = (0*0) - ((2-L)(1) => L-2 = 0 => L = 2

 

[Dick]

If you are expanding along the first row, there are two nonvanishing cofactors. There's an L in the first column and a 1 in the last.

 

[cscott]

Oops. Alright thanks.