Originally Posted by

**calculuskid1** So I've been doing this for a VERY long time now I don't seem to be getting the right answer (according to online solvers) I'm wondering if you guys can spot my error because this is REALLY frustrating.

$\displaystyle A=\left(\begin{matrix} 2/5&1/5\\3 &0\end{matrix}\right)$

And I found one of the Eigenvalues to be 1. so now subtracting the Diagonal from 1 I get this and I start to solve the homogeneous system of equation.

$\displaystyle (L=1)=\left(\begin{matrix} 3/5&1/5\\3 &1\end{matrix}\right)$ = $\displaystyle \left(\begin{matrix} 3&1\\3 &1\end{matrix}\right)$ = $\displaystyle \left(\begin{matrix} 1&1/3\\0 &0\end{matrix}\right)$

Now from here x(2)=T and x(1)+(1/3)T=0 --->X(1)=(-1/3)T

SO $\displaystyle X=\left(\begin{matrix} -1\\3\end{matrix}\right)$ BUT according toe the online solver it should be $\displaystyle X=\left(\begin{matrix} 1\\3\end{matrix}\right)$

I have tried everything so I need someone's help, WHAT AM I DOING WRONG?

Thank you!