Q. 10 - Precalculus Enhanced with Graphing Utilities

Question

Find the value of the determinant.

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

Step-by-Step Solution

Answer

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

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 = a b c d = a ⋅ d - c ⋅ b .

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