- #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: [tex]\Omega[/tex] =
[tex]\left[ {\begin{array}{ccc}
2 & 0 & 0 \\
0 & 3 & -1 \\
0 & -1 & 3 \\
\end{array} } \right]
[/tex]
Show that [tex]\omega[/tex]1 = [tex]\omega[/tex]2 = 1; [tex]\omega[/tex]3 = 2
So det([tex]\Omega[/tex] - [tex]\omega[/tex]I) = (2 - [tex]\omega[/tex])((3 - [tex]\omega[/tex])(3 - [tex]\omega[/tex]) - 1)
Which obviously leaves [tex]\omega[/tex] = 2, but also (3 - [tex]\omega[/tex])2 = 1, the solutions to which should be [tex]\omega[/tex] = 2 and [tex]\omega[/tex] = 4.
Where am I going wrong?
Any help greatfully appreciated.
Homework Statement
Given the matrix: [tex]\Omega[/tex] =
[tex]\left[ {\begin{array}{ccc}
2 & 0 & 0 \\
0 & 3 & -1 \\
0 & -1 & 3 \\
\end{array} } \right]
[/tex]
Show that [tex]\omega[/tex]1 = [tex]\omega[/tex]2 = 1; [tex]\omega[/tex]3 = 2
Homework Equations
The Attempt at a Solution
So det([tex]\Omega[/tex] - [tex]\omega[/tex]I) = (2 - [tex]\omega[/tex])((3 - [tex]\omega[/tex])(3 - [tex]\omega[/tex]) - 1)
Which obviously leaves [tex]\omega[/tex] = 2, but also (3 - [tex]\omega[/tex])2 = 1, the solutions to which should be [tex]\omega[/tex] = 2 and [tex]\omega[/tex] = 4.
Where am I going wrong?
Any help greatfully appreciated.