To add two or more matrices together, they need to have the same size or order. Once this is verified, we can add the matrices together by finding the sum of the corresponding elements. When we subtract matrices together, we will also need to make sure the two matrices are the same size. We can then subtract corresponding elements in the correct order.

Test Objectives
• Demonstrate the ability to add matrices
• Demonstrate the ability to subtract matrices
• Demonstrate the ability to solve a matrix equation
Adding and Subtracting Matrices Practice Test:

#1:

Instructions: find A + B.

$$a)\hspace{.2em}$$ $$A=\left[ \begin{array}{cc}3 & 1\\ 5 & 7\end{array}\right]$$ $$B=\left[ \begin{array}{cc}-1 & -4\\ 5 & 6\end{array}\right]$$

$$b)\hspace{.2em}$$ $$A=\left[ \begin{array}{cc}-3 & 14\\ 18 & -1\end{array}\right]$$ $$B=\left[ \begin{array}{cc}-7 & 8\\ 13 & 11\end{array}\right]$$

#2:

Instructions: find A + B.

$$a)\hspace{.2em}$$ $$A=\left[ \begin{array}{ccc}-2 & 4 & 5\\ 8 & 1 & 6 \\ 12 & 19 & 5\end{array}\right]$$ $$B=\left[ \begin{array}{ccc}-2 & 1 & 5\\ 9 & 4 & -3 \\ 5 & 8 & 6\\ -1 & 7 & 6\end{array}\right]$$

$$b)\hspace{.2em}$$ $$A=\left[ \begin{array}{ccc}1 & 9 & -2\\ -6 & 3 & -5 \\ 27 & -20 & 11\end{array}\right]$$ $$B=\left[ \begin{array}{ccc}-1 & -9 & 2\\ 6 & -3 & 5 \\ -27 & 20 & -11\end{array}\right]$$

#3:

Instructions: find A - B.

$$a)\hspace{.2em}$$ $$A=\left[ \begin{array}{cc}8 & 3\\ 2 & -4\\ 1 & -11\end{array}\right]$$ $$B=\left[ \begin{array}{cc}1 & 10\\ 4 & 9\\ -2 & 11\end{array}\right]$$

$$b)\hspace{.2em}$$ $$A=\left[ \begin{array}{ccc}-1 & -3 & -4\\ 20 & 5 & 7 \\ 19 & 15 & 27\end{array}\right]$$ $$B=\left[ \begin{array}{ccc}9 & 10 & 12\\ 5 & 1 & 8 \\ 3 & 6 & 5\end{array}\right]$$

#4:

Instructions: find A - B.

$$a)\hspace{.2em}$$ $$A=\left[ \begin{array}{ccc}3 & 0 & 1\\ -1 & 8 & 0 \\ -99 & 13 & 7\end{array}\right]$$ $$B=\left[ \begin{array}{ccc}4 & 12 & 8 & -1\\ -5 & 10 & 9 & -2 \\ -2 & 14 & 1 & -3\end{array}\right]$$

Instructions: A + X = B, find X.

$$b)\hspace{.2em}$$ $$A=\left[ \begin{array}{cc}-2 & 4\\ 17 & 5\end{array}\right]$$ $$B=\left[ \begin{array}{cc}3 & -5\\ 8 & 7\end{array}\right]$$

#5:

Instructions: A + X = B, find X.

$$a)\hspace{.2em}$$ $$A=\left[ \begin{array}{cc}-5 & -14 & 13\\ 9 & -7 & 11\end{array}\right]$$ $$B=\left[ \begin{array}{cc}-1 & 2\\ 3 & 4\\ 6 & -9\end{array}\right]$$

Instructions: A - X = B, find X.

$$b)\hspace{.2em}$$ $$A=\left[ \begin{array}{ccc}-3 & 7 & 2\\ -2 & 0 & -1 \\ 3 & 4 & 0\end{array}\right]$$ $$B=\left[ \begin{array}{ccc}15 & 19 & 0\\ 14 & -7 & -1\\ 22 & 13 & 8\end{array}\right]$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}$$ $$\left[ \begin{array}{cc}2 & -3\\ 10 & 13\end{array}\right]$$

$$b)\hspace{.2em}$$ $$\left[ \begin{array}{cc}-10 & 22\\ 31 & 10\end{array}\right]$$

#2:

Solutions:

a) Doesn't exist

b) 03 x 3

#3:

Solutions:

$$a)\hspace{.2em}$$ $$\left[ \begin{array}{cc}7 & -7\\ -2 & -13 \\ 3 & -22\end{array}\right]$$

$$b)\hspace{.2em}$$ $$\left[ \begin{array}{cc}-10 & -13 & -16\\ 15 & 4 & -1 \\ 16 & 9 & 22\end{array}\right]$$

#4:

Solutions:

a) Doesn't exist

$$b)\hspace{.2em}$$ $$X=\left[ \begin{array}{cc}5 & -9\\ -9 & 2\end{array}\right]$$

#5:

Solutions:

a) No Solution

$$b)\hspace{.2em}$$ $$A=\left[ \begin{array}{cc}-18 & -12 & 2\\ -16 & 7 & 0 \\ -19 & -9 & -8\end{array}\right]$$