I needed to find for which values of $\lambda$ the matrix is singular.
$ \begin{bmatrix} 1-\lambda & 0 & 3 \\ 1 & 1-\lambda & 0 \\ 0 & 2 & -\lambda \\ \end{bmatrix} $
What I did : Compared the determinant of the matrix to zero and ended up with this: $-\lambda (1-2\lambda+\lambda^2)+6=0 $ (tried 2 different ways of calculating the determinant but ended up with the same expression). How do I solve it from here? Thanks a lot!