Chapter 8.3, Problem 21E

To determine

To evaluate:The inverse of the given matrix if possible.

Explanation of Solution

Given information:The given matrix is

  $\left[\begin{array}{ccc}-5& 0& 0\\ 2& 0& 0\\ -1& 5& 7\end{array}\right]$ .

Calculation:

To check that the inverse of matrix is possible, calculate the determinant of the matrix. If determinant is not equal to zero then inverse exist.

The determinant of the given matrix is:

  $\begin{array}{c}\left|\begin{array}{ccc}-5& 0& 0\\ 2& 0& 0\\ -1& 5& 7\end{array}\right|=-5\left(0-0\right)-0\left(14-0\right)+0\left(10-0\right)\\ =0\end{array}$

Therefore, the inverse of the given matrix is not possible.