Chapter 7, Problem 136RE

To determine

To find: the inverse of the matrix using a graphing utility.

Answer to Problem 136RE

The inverse of the matrix $A$ is

  $\left[\begin{array}{cc}\frac{1}{23}& \frac{5}{23}\\ -\frac{2}{23}& \frac{3}{46}\end{array}\right]$

Explanation of Solution

Given information:

Given matrix

  $\left[\begin{array}{cc}3& -10\\ 4& 2\end{array}\right]$

Calculation:

Using graphing calculator:

Select the matrix from the MATRX EDIT menu and enter the dimensions.

  

The center portion of the matrix editor displays up to four rows and four columns of a matrix.

The display of the matrix is shown below,

  

This is a $2\times 2$ matrix.

To display the centers of a matrix on the home screen, select the matrix from the MATRX NAMES menu, and then press ENTER.

The matrix will be displayed as below,

  

Now the inverse of the matrix is obtained by pressing $x^{-1}$ key and then ENTER.

  

Since the answer is displayed in decimals we can convert them into fractions.

To convert the decimals into fractions select the MATH menu and then press Frac option.

The screen is shown below:

  

Therefore, the inverse of the matrix $A$ is

  $\left[\begin{array}{cc}\frac{1}{23}& \frac{5}{23}\\ -\frac{2}{23}& \frac{3}{46}\end{array}\right]$