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

Show that $$\omega$$₁ = $$\omega$$₂ = 1; $$\omega$$₃ = 2

Homework Equations

The Attempt at a Solution

So det($$\Omega$$ - $$\omega$$I) = (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