## Algebra and Trigonometry 10th Edition

$e^{-2x}$
The determinant of a $2 \times 2$ matrix can be computed by using the formula $det =ps-qr$ where $det =\begin{bmatrix}p & q \\r & s\end{bmatrix}$ After simplifying, the determinant of this matrix will be: $det =(e^{-x})((1-x)e^{-x})+(e^{-x})x(e^{-x})$ or, $=e^{-2x}-xe^{-2x}+xe^{-2x}$ or, $=e^{-2x}$