Q53. - Algebra 2

Question

Find the inverse of each matrix, if it exists.

 $\left[\begin{array}{cc}-3& 2\\ -6& 4\end{array}\right]$

Step-by-Step Solution

Answer

The inverse of the given matrix does not exist.

Step 1. Given Information.

Given, to find the inverse of the matrix  $\left[\begin{array}{cc}-3& 2\\ -6& 4\end{array}\right]$.

Step 2. Calculation .

The inverse of matrix  $A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ is  $A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{cc}d& -b\\ -c& a\end{array}\right]$, where  $ad-bc\ne 0$:

Here  $a=-3,b=2,c=-6,d=4$.

 

Checking if the inverse exists:

 

 $\begin{array}{l}ad-bc=\left(-3\right)\left(4\right)-\left(2\right)\left(-6\right)\\ ad-bc=-12+12\\ ad-bc=0\end{array}$

Hence, the inverse does not exists.

Step 3. Conclusion .

Hence, the inverse of the given matrix does not exist.