$$ \begin{bmatrix} 4 & \frac {69}{28} \\ \frac {69}{28} & \frac {15}{7} \\ \end{bmatrix} $$ This is my initial matrix. So, I calculated my eigenvalues with no problem but got stuck with eigenvectors. My eigenvalues are 5.7049 and 0.4380 (they are right - I checked with Matlab).
Then I performed row manipulation and got
$$ \begin{bmatrix} -1.70631 & 2.464 \\ 0 & 0 \\ \end{bmatrix} $$
And now I don't know what to do to get the correct eigenvectors. There's one free variable so I set $x_1$ as 't' and tried solving for $x_2$ but that gives me the correct answer. According to Matlab, the correct eigenvector should be $$ \begin{bmatrix} -0.8224 \\ 0.5689\\ \end{bmatrix} $$
What do I have to do to get that??
Thanks in advance:)