I was solving a mechanics problem, and eventually obtained this matrix:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\begin{vmatrix}

1-\Omega^2 & -1 & -1/2 & 0 & 0 & 0\\

-1 & 3/2 -\Omega^2 & 0 & 0 & -1/2 & 1/2\\

0 & -1/2 & 1/2-\Omega^2 & 0 & 1/2 & -1/2\\

0 & 0 & 0 & 1-\Omega^2 & 0 & -1\\

0 & -1/2 & 1/2 & 0 & 1/2-\Omega^2 & -1/2\\

0 & 1/2 & -1/2 & -1 & -1/2 & 3/2-\Omega^2

\end{vmatrix} = 0

[/tex]

I must find the roots [tex]\Omega^2[/tex]. The textbook gives a hint that I should rearrange columns to show that there is a triple root [tex]\Omega^2 = 0[/tex], and then reduce the matrix to 3x3 and then the determinant is easy from there. I'm able to switch columns back and forth, but I don't know how to find any triple roots from that. I'm pretty new to matrices. Could you give me some useful properties or anything else that would be helpful?

Oh, and the matrix may be wrong, but not too much wrong, maybe just a few elements... Notice that it's symmetric.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Secular equation, 6x6 matrix

**Physics Forums | Science Articles, Homework Help, Discussion**