Question

Find the value of the determinant.

$\left|\begin{array}{cc}-3& -1\\ 4& 2\end{array}\right|$

Short answer

$\left|\begin{array}{cc}-3& -1\\ 4& 2\end{array}\right|=-2$

Step-by-step solution

Step 1. Given information 

We have been given:

$\left|\begin{array}{cc}-3& -1\\ 4& 2\end{array}\right|$

We have to find the value of this determinant.

Step 2. Use formula D=abcd=a⋅d-c⋅b.

$$\begin{gathered} \left|\begin{array}{cc}-3& -1\\ 4& 2\end{array}\right|=-3\times 2-4\times (-1) \\ =-6+4 \\ =-2 \end{gathered}$$