Chapter 8, Problem 147RE

To determine

Find the inverse of the given matrix using a graphing utility and explain about the message appears on the screen.

Answer to Problem 147RE

The matrix is not invertible.

Explanation of Solution

Given information:

The given matrixis $\left[\begin{array}{cc}1& -3\\ -2& 6\end{array}\right]$ .

Calculation:

Use a graphing calculator.

Open a calculator and select the $2\times 2$ matrix box.

  $\left[\begin{array}{cc}& \\ & \end{array}\right]$

Enter the given data.

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

Enter “Find the inverse” button.

The resulting display on the screen is that the determinant is $0$ , the matrix is not invertible.

The explanation about the message appears on the screen is given below.

If $A$ is $2\times 2$ matrix

  $A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$

Then

  $A$ is invertible if and only if

  $ad-bc\ne 0$ . Moreover,

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

  $ad-bc$ is the determinant of the given matrix.