Chapter 11.4, Problem 67AYU

To determine

The inverse of the matrix $\left[\begin{array}{ccc}25& 61& -12\\ 18& -12& 7\\ 3& 4& -1\end{array}\right]$ by using graphing utility if it exists.

Answer to Problem 67AYU

Solution:

The inverse of the matrix $\left[\begin{array}{ccc}25& 61& -12\\ 18& -12& 7\\ 3& 4& -1\end{array}\right]$ is $\left[\begin{array}{ccc}-0.02& 0.02& 0.41\\ 0.06& 0.02& -0.57\\ 0.16& 0.12& -2.05\end{array}\right]$.

Explanation of Solution

Given information:

The matrix, $\left[\begin{array}{ccc}25& 61& -12\\ 18& -12& 7\\ 3& 4& -1\end{array}\right]$.

Explanation:

Use the steps below to find the inverse of the matrix using graphing calculator.

Step I: Press the ON key.

Step II: Press [2ND][$x^{-1}$] to access the calculate menu.

Step III: Move curser to the “EDIT” menu at the top and press [ENTER].

Step IV: Select the size of the matrix that is number of rows by number of columns. Then plug the entries in that matrix form left to right. After each number press [ENTER] to go the next spot.

Step V: Press [2ND] [MODE] and go back into the matrix menu by clicking [2ND] and [ $x^{-1}$] then press [1] and [ENTER].

Step VI: Press the inverse key [$x^{-1}$] and press [ENTER].

The obtained inverse as follows:

$\left[\begin{array}{ccc}-0.02343& 0.01903& 0.41435\\ 0.05710& 0.01611& -0.57247\\ 0.15813& 0.12152& -2.04685\end{array}\right]$

By rounding numbers to the two decimal places,

$\left[\begin{array}{ccc}-0.02& 0.02& 0.41\\ 0.06& 0.02& -0.57\\ 0.16& 0.12& -2.05\end{array}\right]$

Thus, the inverse of the matrix $\left[\begin{array}{ccc}25& 61& -12\\ 18& -12& 7\\ 3& 4& -1\end{array}\right]$ is $\left[\begin{array}{ccc}-0.02& 0.02& 0.41\\ 0.06& 0.02& -0.57\\ 0.16& 0.12& -2.05\end{array}\right]$.