1. ## [SOLVED] eigen vectors

i have found the eigenvalues from

A= |1 2|
|5 4|

as -1 and 6.

then for the eigenvectors

then |-5 2| |x1|=0
|5 -2| |x2|=0

so x1 = 2/5 x2

but from here how do i get the eigenvetor of (2/5) ?

2. Originally Posted by ben35
i have found the eigenvalues from

A= |1 2|
|5 4|

as -1 and 6.

then for the eigenvectors

then |-5 2| |x1|=0
|5 -2| |x2|=0

so x1 = 2/5 x2

but from here how do i get the eigenvetor of (2/5) ?
You are incorrect about your last step. You sub the eigenvalue into the equation
$\displaystyle \left [ \begin{matrix} 1 & 2 \\ 5 & 4 \end{matrix} \right ] \cdot \left [ \begin{matrix} x_1 \\ x_2 \end{matrix} \right ] = \lambda \left [ \begin{matrix} x_1 \\ x_2 \end{matrix} \right ]$

So for the eigenvalue $\displaystyle \lambda = 6$ you have:
$\displaystyle \left [ \begin{matrix} 1 & 2 \\ 5 & 4 \end{matrix} \right ] \cdot \left [ \begin{matrix} x_1 \\ x_2 \end{matrix} \right ] = 6 \left [ \begin{matrix} x_1 \\ x_2 \end{matrix} \right ]$

Which says that
$\displaystyle x_1 + 2x_2 = 6x_1$
and
$\displaystyle 5x_1 + 4x_2 = 6x_2$

and you can solve this from there.

-Dan