Question

find the value of each determinant.

$\left|\begin{array}{cc}-2& 5\\ 3& 7\end{array}\right|$

Short answer

The determinant of the given matrix is$-29$.

Step-by-step solution

Step 1. Given

$\left|\begin{array}{cc}-2& 5\\ 3& 7\end{array}\right|$

Step 2. Calculation

$$\begin{gathered} \left|\begin{array}{cc}-2& 5\\ 3& 7\end{array}\right| \\ =\left(-2\right)\left[7\right]-5\left[3\right] \\ =-14-15 \\ =-29 \end{gathered}$$