Q. 64 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 61– 66, show that each matrix has no inverse 

$\left[\begin{array}{rr}-3& 0\\ 4& 0\end{array}\right]$

Step-by-Step Solution

Answer

The given matrix has no inverse. 

Step 1. Given information

A matrix is given as, 

$\left[\begin{array}{rr}-3& 0\\ 4& 0\end{array}\right]$

Step 2. Finding the inverse.

To find the inverse,

$$\begin{gathered} \left[A\mid I_2\right]=\left[\begin{array}{cccc}-3& 0& 1& 0\\ 4& 0& 0& 1\end{array}\right] \\ \left\{R_1\to \frac{R_1}{-3}\right\} \\ \left[\begin{array}{cccc}1& 0& -\frac{1}{3}& 0\\ 4& 0& 0& 1\end{array}\right] \\ \left\{R_2\to R_2-4R_1\right\} \\ \left[\begin{array}{llll}1& 0& -\frac{1}{3}& 0\\ 0& 0& \frac{4}{3}& 1\end{array}\right] \end{gathered}$$

Since the left side does not represent an identity matrix, therefore, inverse does not exist.