Question

Find the value of each determinant.

7.$\left|\begin{array}{cc}7& 8\\ 3& -2\\ & \end{array}\right|$

Short answer

The value of the determinant$\left|\begin{array}{cc}7& 8\\ 3& -2\\ & \end{array}\right|=-38$.

Step-by-step solution

- Define the determinant of second-order matrix

The determinant of second order matrix is found by calculating the difference of the product of the two diagonals, that is., $\left|\begin{array}{cc}a& b\\ c& d\\ & \end{array}\right|=ad-bc$.

- Find the determinant

Apply the definition of the method of finding determinant of second order matrix $\left|\begin{array}{cc}7& 8\\ 3& -2\\ & \end{array}\right|$.

$\left|\begin{array}{cc}7& 8\\ 3& -2\\ & \end{array}\right|=7\times \left(-2\right)-8\left(3\right)$

- Simplify

To further simplify multiply the values first and then find the difference.

$\begin{array}{c}\left|\begin{array}{cc}7& 8\\ 3& -2\end{array}\right|=7\times (-2)-8\left(3\right)\\ =-14-24\\ =-38\end{array}$