## Precalculus (6th Edition) Blitzer

$\left| \begin{matrix} 1 & 1 & 1 \\ 2 & 2 & 2 \\ -3 & 4 & -5 \\ \end{matrix} \right|$ Include the 2 common from ${{R}_{2}}$. The determinant will be as here $2\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ -3 & 4 & -5 \\ \end{matrix} \right|$ Here, ${{R}_{1}}$ and ${{R}_{2}}$ are similar. Therefore, $\left| \begin{matrix} 1 & 1 & 1 \\ 2 & 2 & 2 \\ -3 & 4 & -5 \\ \end{matrix} \right|=0$