Question

Find the value of each determinant.

$\left|\begin{array}{cc}-3& -6\\ 4& 8\end{array}\right|$

Short answer

The value of the determinant$\left|\begin{array}{cc}-3& -6\\ 4& 8\end{array}\right|=0$.

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

Expand the determinant .

$\left|\begin{array}{cc}-3& -6\\ 4& 8\end{array}\right|=-3\times \left(8\right)-4\left(-6\right)$

- Simplify

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

$\begin{array}{c}\left|\begin{array}{c}\begin{array}{cc}-3& -6\\ 4& 8\end{array}\end{array}\right|=-3\times \left(8\right)-4(-6)\\ =-24+24\\ =0\end{array}$