Chapter 11, Problem 34RE

To determine

To calculate: the inverse of the matrices given .

Answer to Problem 34RE

Solution: Singular Matrix

Explanation of Solution

  $A=\left[\begin{array}{cc}\begin{array}{l}-3\\ -6\end{array}& \begin{array}{l}1\\ 2\end{array}\end{array}\right]$

Using the given formula to calculate the inverse of the matrix:-

  $\begin{array}{l}{A}^{-1}=\frac{1}{D}\left[\begin{array}{cc}\begin{array}{l}d\\ -c\end{array}& \begin{array}{l}-b\\ a\end{array}\end{array}\right]\\ D=ad-bc\ne 0\end{array}$

  $D=(-3)\times 2-(-6)\times 1=0$

Hence, the matrix is singular and there is no inverse.