Chapter 11.3, Problem 1AYU

3

To determine

To fill: The blank in the statement, “ $D=\begin{array}{cc}a& b\\ c& d\end{array}=\_\_\_\_\_\_\_$ ”.

Answer to Problem 1AYU

The complete statement is, “ $\begin{array}{c}D=\begin{array}{cc}a& b\\ c& d\end{array}\\ =ad-bc\end{array}$ ”.

Explanation of Solution

Given information:

The statement, “ $D=\begin{array}{cc}a& b\\ c& d\end{array}=\_\_\_\_\_\_\_$ ”.

Consider the provided statement, “ $D=\begin{array}{cc}a& b\\ c& d\end{array}=\_\_\_\_\_\_\_$ ”.

Since the above determinate have 2 rows ad 2 columns. Recall that to solve $2\times 2$ determinate first multiply entries of principal diagonal and then subtract other diagonal entries multiplication from it.

So,

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

Therefore, the complete statement is, “ $\begin{array}{c}D=\begin{array}{cc}a& b\\ c& d\end{array}\\ =ad-bc\end{array}$ ”.