Chapter 11.3, Problem 8AYU

$\left[\begin{array}{l}\begin{array}{cc}8& -3\end{array}\\ \begin{array}{cc}4& 2\end{array}\end{array}\right]$

To determine

To find: The value of the determinant $\left|\begin{array}{cc}8& -3\\ 4& 2\end{array}\right|$.

Answer to Problem 8AYU

28

Explanation of Solution

Given:

$\left|\begin{array}{cc}8& -3\\ 4& 2\end{array}\right|$

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:

$D=\left|\begin{array}{cc}8& -3\\ 4& 2\end{array}\right|=8\times 2-\left(-3\right)\times 4=16+12=28$