Question

Find the value of the determinant.

$\left|\begin{array}{cc}-4& 2\\ -5& 3\end{array}\right|$

Short answer

$\left|\begin{array}{cc}-4& 2\\ -5& 3\end{array}\right|=-2$

Step-by-step solution

Step 1. Given information 

We have been given:

$\left|\begin{array}{cc}-4& 2\\ -5& 3\end{array}\right|$

We have to find the value of this determinant.

Step 2. Use formula D=abcd=a⋅d-c⋅b.

$$\begin{gathered} \left|\begin{array}{cc}-4& 2\\ -5& 3\end{array}\right|=-4\times 3-(-5)\times 2 \\ =-12+10 \\ =-2 \end{gathered}$$