Q48. - Algebra 2

Question

The x $\boxed{x^{-1}}$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.

 

$\left[\begin{array}{cc}12& 4\\ 15& 5\end{array}\right]$

Step-by-Step Solution

Answer

The required inverse does not exist.

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.

 $\begin{array}{l}\text{MATRIX}\left[\text{A}\right]3\times 3\\ \left[\begin{array}{cc}12& 4\\ 15& 5\end{array}\right]\end{array}$

Step 2 – 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.

 

$\begin{array}{l}\text{ERR}:\text{SINGULAR MAT}\\ 1:\text{Quit}\\ 2:\mathrm{Goto}\end{array}$

Step 3 – Make the conclusion

As the calculator is showing error which means that the inverse of the provided matrix does not exist.