Chapter 11.3, Problem 1AYU

$D=\left[\begin{array}{l}\begin{array}{cc}a& b\end{array}\\ \begin{array}{cc}c& d\end{array}\end{array}\right]=$ _______.

To determine

To fill: $D=\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=$ _____.

Answer to Problem 1AYU

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

Explanation of Solution

Given:

$D=\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|$

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:

By the given concept we get,

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