- #1
TimID
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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
Given the matrix: \Omega =
\left[ {\begin{array}{ccc}<br /> 2 & 0 & 0 \\<br /> 0 & 3 & -1 \\<br /> 0 & -1 & 3 \\<br /> \end{array} } \right]<br />
Show that \omega1 = \omega2 = 1; \omega3 = 2
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.
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]<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.
