## Algebra and Trigonometry 10th Edition

$-23$
The general form of a matrix of order $2 \times 2$ is: $det \ A=\begin{vmatrix} p & q \\ r & s\end{vmatrix}=ps-qr$ Since Column-1 has the most zeroes, we choose Column-1. Now, $det \ A =1\begin{vmatrix} 1 & 2 \\ 1 & -2 \end{vmatrix}-(-4) 1\begin{vmatrix} 1 & 4 \\ 1 & -1 \end{vmatrix}+0 =-23$