For the matrix \begin{pmatrix}1/2 & 1 & 3/4\\2/3 & 0 & 0\\0 & 1/3 & 0\end{pmatrix}
Find the eigenvalues and corresponding eigenvectors. I did this with an online calculator and got that there were $2$ complex eigenvalues, but I am struggling to do the work by hand. I know that I have to get it to the characteristic polynomial with the determinant of $A -\lambda \cdot I$ but after that I am lost.