Chapter 3.7, Problem 28PPS

To determine

To find: the determinant of $\left[\begin{array}{cc}-5& 8\\ -6& -7\end{array}\right]$ .

Answer to Problem 28PPS

The determinant of matrix is $83$ .

Explanation of Solution

Given:

The matrix is $\left[\begin{array}{cc}-5& 8\\ -6& -7\end{array}\right]$ .

Calculation:

Write the expression of determinant of matrix as follows:

Consider the matrix A ,

  $A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$

Determinant of matrix is,

  $\left|A\right|=ad-bc$

Consider matrix and determine the determinant as follows:

  $\begin{array}{c}\left|\begin{array}{cc}-5& 8\\ -6& -7\end{array}\right|=\left(-5\right)\times \left(-7\right)-\left(8\right)\times \left(-6\right)\\ =35+48\\ =83\end{array}$

Thus, the determinant of matrix is $83$ .