Chapter 11.3, Problem 10AYU

To determine

To find: The value of the determinant $\left|\begin{array}{cc}-4& 2\\ -5& 3\end{array}\right|$.

Answer to Problem 10AYU

$-2$

Explanation of Solution

Given:

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

Formula used:

To find the value of a second order $2\times 2$ determinant:

$\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=a\times d-b\times c=ad-bc$

Calculation:

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