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Jun26-09, 02:49 AM
P: 13
Quote Quote by Pengwuino View Post
At [tex] \therefore y = -\frac{3}{2}x [/tex], what this is telling you is that the solution to your system of equation is ANY matrix such that the y-entry is -3/2 of the x-entry. For example, you can try [tex]\left( {\begin{array}{*{20}c} 2 \\ { - 3} \\\end{array}}\right)[/tex] for example. Any constant multiple of that eigenvector is an eigenvector as well! You can normalize it and use [tex]
\left( {\begin{array}{*{20}c}
{\frac{2}{{\sqrt {13} }}} \\
{\frac{{ - 3}}{{\sqrt {13} }}} \\
\end{array}} \right)[/tex] for example! Plug it into your original equation and you'll see both work.
I got it right?

Understood! So it can also be
[tex] \left( {\begin{array}{*{20}c} 4 \\ { - 6} \\\end{array}}\right) [/tex] ?