Chapter 16.6, Problem 5OE

To determine

To Check: Whether the given matrix has an inverse:

  $\left[\begin{array}{cc}6& -3\\ -10& 5\end{array}\right]$

Answer to Problem 5OE

No

Explanation of Solution

Given: $\left[\begin{array}{cc}6& -3\\ -10& 5\end{array}\right]$

Formula Used: $\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=ad-cb$

For checking whether a given matrix is invertible it is needed to verify that the determinant of the matrix is non-zero or not.

If the determinant of the given matrix is non-zero then the matrix is invertible.

If the determinant of the matrix is zero, the matrix does not have an inverse.

Finding the determinant of the given matrix:

  $\left|\begin{array}{cc}6& -3\\ -10& 5\end{array}\right|=(6)(5)-(-3)(-10)=30-30=0$

The determinant of the given matrix is zero so the matrix is not invertible.

No, the given matrix does not have an inverse.