## Algebra and Trigonometry 10th Edition

The determinant of a $2 \times 2$ matrix can be computed by using the formula $det =ps-qr$ where $det =\begin{bmatrix}p & q \\r & s\end{bmatrix}$ we have $\begin{bmatrix}2 & -4 & 5 \\1 & -2&3 \\0 & 0& 0\end{bmatrix}$ It can be seen that there is a row of all zeroes. When one row of a matrix is all zeros, then each factor is multiplied by $0$. Thus, the determinant is zero.