[tex]X'=\left[\begin{array}{ccc}4 & 1 & 4\\ 1 & 7 & 1\\ 4 & 1 & 4\end{array}\right]X[/tex](adsbygoogle = window.adsbygoogle || []).push({});

After evaluating the determinant I get from the characteristic equation [itex]\lambda=0[/itex]

[tex]\lambda=\frac{15\pm \sqrt{119}*i}{2}[/tex]

Now here is where I am not sure where to go. I need to create an Eigenvector. I stared it off by plugging in for [itex]\lambda=0[/itex] giving the relationships:

[itex]4k_1+k_2+4k_3=0[/itex]

[itex]k_1+7k_2+k_3=0[/itex]

[itex]4k_1+k_2+4k_3=0[/itex]

Now usually, in the case of a 2x2 matrix, I would solve for let's say k1 in terms of k2 and then just PICK some value for k2 and that would establish my Eigenvector.

I am a little confused as to how to do this with a 3x3. It would appear I have some sort of special case here since row 1 is the same as row 3, but I am unsure how to use that to my advantage?

Could someone just point me toward the next step?

Thanks!!!!

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# Solving 3x3 Matrix of DEs

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