Question

The $\boxed{x^{-1}}$key on a Ti-83 Plus is used to find the inverse of a matrix. If you get a SINGULAR MATRIX error on the screen, then the matrix has no inverse.

Use a graphing calculator to find inverse of each matrix.

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

Short answer

The required inverse is$\left[\begin{array}{cc}0.6& -0.2\\ 0.2& -0.4\end{array}\right]$ .

Step-by-step solution

Step 1- Enter the matrix in the calculator

Press the$\boxed{\text{2nd}}$button on the calculator after it press $\boxed{x^{-1}}$ then go to EDIT menu. By selecting the dimensions of matrix as $2\times 2$ perform the insertion of the provided matrix into the calculator.

$\begin{array}{l}\text{MATRIX}\left[\text{A}\right]3\times 3\\ \left[\begin{array}{cc}2& -1\\ 1& -3\end{array}\right]\end{array}$

– Calculate the inverse

Press the $\boxed{\text{2nd}}$button after the appearance of home screen by pressing $\boxed{\text{2nd}}$button and MODE button. Select the matrix$\left[\text{A}\right]$and press$\boxed{x^{-1}}$ to get the inverse of the matrix.

$\left[\begin{array}{cc}0.6& -0.2\\ 0.2& -0.4\\ & \end{array}\right]$

– Make the conclusion

As the obtained matrix contains the values of provided matrix so obtained inverse is correct.