Thread: Eigenvalues & Eigenvectors View Single Post
P: 13
 Quote by Pengwuino At $$\therefore y = -\frac{3}{2}x$$, 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 $$\left( {\begin{array}{*{20}c} 2 \\ { - 3} \\\end{array}}\right)$$ for example. Any constant multiple of that eigenvector is an eigenvector as well! You can normalize it and use $$\left( {\begin{array}{*{20}c} {\frac{2}{{\sqrt {13} }}} \\ {\frac{{ - 3}}{{\sqrt {13} }}} \\ \end{array}} \right)$$ for example! Plug it into your original equation and you'll see both work.
I got it right?

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