Chapter 3.7, Problem 26PPS

To determine

To find: the determinant of $\left[\begin{array}{cc}-7& 12\\ 5& 6\end{array}\right]$ .

Answer to Problem 26PPS

The determinant of matrix is $-102$ .

Explanation of Solution

Given:

The matrix is $\left[\begin{array}{cc}-7& 12\\ 5& 6\end{array}\right]$ .

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:

  $\begin{array}{c}\left|A\right|=ad-bc\\ =\left(-7\right)\times \left(6\right)-\left(12\right)\times \left(5\right)\\ =-42-60\\ =-102\end{array}$

Thus, the determinant of matrix is $-102$ .