Hi

can someone explain to be how they get the eigenvectors for the following matrix

$\displaystyle \begin{matrix}2 & -1 \\ -4 & 2 \end{matrix}$

$\displaystyle \begin{matrix}1 & \frac{-1}{2} \\ 0 & 0 \end{matrix}$

hence

$\displaystyle v1 = \frac{-1}{2}v2$

$\displaystyle v2 = -2v1$

eigenvalues are $\displaystyle \lambda = 4 \lambda = 0$

i get $\displaystyle \begin{matrix} \frac{-1}{2} \\ -2 \end{matrix}$

however answers says when $\displaystyle \lamba =4 $

matrix is $\displaystyle \begin{matrix} 1 \\ -2 \end{matrix}$

i don't understand how they got this result, someone please explain this to me.

P.S