Finding eigenvalues, Shankar exercise 1.8.3

[TimID]

First, I appologise if this is in the wrong place, while the book is QM, the question is pure maths. Also I'm not sure if this techically counts as homework as I am self studying. Finally, sorry for the poor formatting, I'm not that good with LaTeX

Homework Statement

Given the matrix: \Omega =
\left[ {\begin{array}{ccc}<br /> 2 &amp; 0 &amp; 0 \\<br /> 0 &amp; 3 &amp; -1 \\<br /> 0 &amp; -1 &amp; 3 \\<br /> \end{array} } \right]<br />

Show that \omega₁ = \omega₂ = 1; \omega₃ = 2

Homework Equations

The Attempt at a Solution

So det(\Omega - \omegaI) = (2 - \omega)((3 - \omega)(3 - \omega) - 1)

Which obviously leaves \omega = 2, but also (3 - \omega)² = 1, the solutions to which should be \omega = 2 and \omega = 4.

Where am I going wrong?

Any help greatfully appreciated.

 

[vela]

You're not going wrong for the given matrix. Are you sure you're doing the right problem?

 

[TimID]

You're absolutely right, there was a factor of a half in the original question that I completely missed, thanks. I must have checked the original problem a dozen times before posting and didn't spot it, I hate my brain sometimes.

Thanks again,

Tim