Hi, I'm wondering if there is some kind of shortcut for finding the eigenvalues and eigenvectors of the following matrix.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

C = \left[ {\begin{array}{*{20}c}

{0.8} & {0.3} \\

{0.3} & {0.7} \\

\end{array}} \right]

[/tex]

Solving the equation [tex]\det \left( {C - \lambda I} \right) = 0[/tex], I get [tex]\lambda = \frac{{15 \pm \sqrt {37} }}{{20}}[/tex] and then if I try to find the eigenvectors by finding the solution space of [C - (eigenvalues)I] I end up with what seems like an endless/tedious/time consuming/frustrating bunch of row operations which don't appear to lead anywhere. I'm wondering if there is an easier way to find the eigenvalues, perhaps that might reveal an easier way to find the eigenvectors. Thanks...

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# Eigenvalues of a 2 by 2 matrix

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