Chapter C, Problem 1ES

To determine

Evaluate the determinants.

Answer to Problem 1ES

Solution:

The value of the determinant is 1.

Explanation of Solution

Given:

The given determinant is $\left|\begin{array}{cc}5& 7\\ 2& 3\end{array}\right|$ .

Formula Used:

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

Calculation:

Every square matrix is a real number called the determinant of the matrix. It is denoted by $\det A$ .

First, compare the given determinant of the matrix with the general determinant of the matrix $\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|$ , we get

For this determinant, $a=5,b=7,c=2\text{and}d=3$ .

  $\begin{array}{c}\left|\begin{array}{cc}5& 7\\ 2& 3\end{array}\right|=\left(5\right)\left(3\right)-\left(7\right)\left(2\right)\\ =15-14\\ =1\end{array}$

Conclusion:

The value of the determinant is 1.