#### Answer

.

#### Work Step by Step

Take
$A=\left[ \begin{matrix}
4 & 0 \\
-3 & 5 \\
0 & 1 \\
\end{matrix} \right], \\
B=\left[ \begin{matrix}
5 & 1 \\
-2 & -2 \\
\end{matrix} \right]\text{, and }\\
C=\left[ \begin{matrix}
1 & -1 \\
-1 & 1 \\
\end{matrix} \right].$
The steps to enter and calculate the matrices by using a graphical utility are given below:
Step 1: Go to the matrix above the $\left[ {{x}^{-1}} \right]$ key.
Step 2: Press the arrow to the right of EDIT to allow for entering the matrix.
Step 3: Type in the dimensions of the matrix and enter the values and press ENTER.
Step 4: Repeat the process for the second matrix.
Step 5: Press the arrow to the right to EDIT and choose a new name.
Step 6: Type in the dimensions of the matrix and enter the values and press ENTER.
Step 7: Return to the home screen. Go to MATRIX to get the names of the matrices for adding, subtracting, or multiplying.
Step 8: Choose the mathematical operation (addition, subtraction, or multiplication) and press ENTER to get the answer on the screen.
The difference of A−C cannot be obtained because the orders of the matrices are different.
The difference of B−A cannot be obtained because the orders of the matrices are different.
The solutions calculated in Exercises 37–44 are as follows:
(37)
$\left[ \begin{matrix}
17 & 7 \\
-5 & -11 \\
\end{matrix} \right]$
(38)
$\left[ \begin{matrix}
-5 & -7 \\
-1 & 9 \\
\end{matrix} \right]$
(39)
$\left[ \begin{matrix}
11 & -1 \\
-7 & -3 \\
\end{matrix} \right]$
(40)
$\left[ \begin{matrix}
24 & 0 \\
-33 & -5 \\
-3 & -1 \\
\end{matrix} \right]$
(41)
Since A and C are of different order, their difference cannot be calculated.
(42)
Since B and A are of different order, their difference cannot be calculated.
(43)
$\left[ \begin{matrix}
16 & -16 \\
-12 & 12 \\
0 & 0 \\
\end{matrix} \right]$
(44)
$\left[ \begin{matrix}
28 & 12 \\
-56 & -24 \\
-7 & -3 \\
\end{matrix} \right]$
Since, the solutions calculated manually and the ones calculated using a graphing utility are the same, therefore they are verified to be the same.