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# eigenvalues of matrix watch

1. matrix is:

0,0,1
1,0,0
0,1,0

Find eigenvalues of matrix.

Really stuck on how to do this as I work it out using the only method I know and get (0-λ ) (λ^2) + (λ ). Obviously a solution is 1 but I need to find two more??
2. I'm not sure your characteristic equation is right, shouldn't it be λ^3 - 1?

But yes, you need 3 eigenvalues for a 3*3 matrix (some can be repeated)
3. rearrange to form 3x3I_n ---> triangluar, eigenvalues =1
4. how do you get λ^3 - 1 then?? have I got it wrong? I am not sure what I am doing and only have one example to work from!

thanks.
5. Well by doing it the way you presumably did it (I guess it'd be 1-λ^3 actually), the last term in your expression should be 1*(1*1 - 0 *(0-λ)) = 1, not λ as you have

Remember the eigenvalues can be complex as well, so you don't want to just write λ = 1 as a repeated solution

EDIT/ That smiley thing should be a λ,dunno why it isn't working
6. (Original post by MC REN)
Remember the eigenvalues can be complex as well, so you don't want to just write λ = 1 as a repeated solution
In the question it says find the eigenvalues of the matrix, one of the eigenvalues is real and the remaining two are complex. Find the eigenvector corresponding to the real eigenvalue.

pleeeasee Can you explain how you got your answer and how I go about getting the complex eigenvalues?????

thanks
7. -Write down the matrix and then subtract λ from each of the diagonal terms
-Set the determinant of this to zero, to get the characteristic equation (λ^3 - 1 = 0), which you nearly had - I'm fairly certain you'd just a slight mistake in the algebra
-Solve this equation for λ (hint: )

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