Two eigenvalue for $$A= \begin{pmatrix} .0144&.0117\\ .0117&.0146\\ \end{pmatrix} $$ is $\lambda_1=0.026200427$ and $\lambda_2=0.002799573$.
I have computed the normalized eigenvector for $\lambda_1$. But for $\lambda_2$ I can't. Here is my attempt :
$$\mathbf A\mathbf x= \lambda_2 \mathbf x$$
$$ \begin{pmatrix} .0144&.0117\\ .0117&.0146\\ \end{pmatrix} \begin{pmatrix} x_1\\ x_2\\ \end{pmatrix}=0.002799573\begin{pmatrix} x_1\\ x_2\\ \end{pmatrix}$$
$$.0144 x_1+.0117 x_2=0.002799573 x_1$$ $$.0117 x_1+.0146 x_1=0.002799573 x_2$$
and after simplification first equation yields ,
$$x_1=-0.948240875 x_2$$
and second equation yields ,
$$x_1=-1.00858359 x_2.$$ This two equations don't match. Consequently arbitrarily choosing $x_2=1$ produces two different value of $x_1$.
Where am I doing mistake? I did it several times.
Thanks in advance.