# matrix eigenvalues **URGENT**

• Nov 16th 2008, 06:09 AM
geo3
matrix eigenvalues **URGENT**
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??

Thanks.
• Nov 16th 2008, 06:39 AM
Rapha
Quote:

Originally Posted by geo3
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 ).

no, this is wrong

you get 1-t^3 and therefor one eigenvalue is +1

Quote:

Originally Posted by geo3
Obviously a solution is 1 but I need to find two more??

No, you do not.
• Nov 16th 2008, 06:45 AM
geo3
how did you calculate 1-t^3??
• Nov 16th 2008, 06:46 AM
geo3
Quote:

Originally Posted by Rapha

you get 1-t^3

I am trying to do this of one example I have so if you could explain/show workings that would be great.
• Nov 16th 2008, 06:50 AM
Rapha
$\displaystyle det \begin{pmatrix} 0-t & 0 & 1 \\ 1 & 0 -t & 0 \\ 0&1&0-t \end{pmatrix}$

$\displaystyle det \begin{pmatrix} -t & 0 & 1 \\ 1 & -t & 0 \\ 0&1&-t \end{pmatrix}$

Sarrus:

(-t)*(-t)*(-t) + 0*0*0 + 1*1*1 - 1*(-t)*0 - 0*1*(-t) - (-t)*0*1 = -t^3 +1