Matrix Addition and Subtraction practice worksheet with eight problems for math students.

Problem: Matrix Addition and Subtraction

We are tasked with solving the given matrix addition and subtraction problems. Let's solve each problem step by step.

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#### Problem 1:
$$
\begin{bmatrix}
1 & 1 \\
-3 & 1
\end{bmatrix}
+
\begin{bmatrix}
5 & 2 \\
0 & 1
\end{bmatrix}
$$

Solution:
To add two matrices, we add their corresponding elements.

$$
\begin{bmatrix}
1 + 5 & 1 + 2 \\
-3 + 0 & 1 + 1
\end{bmatrix}
=
\begin{bmatrix}
6 & 3 \\
-3 & 2
\end{bmatrix}
$$

Answer:
$$
\boxed{\begin{bmatrix}
6 & 3 \\
-3 & 2
\end{bmatrix}}
$$

---

#### Problem 2:
$$
\begin{bmatrix}
1 & -6 \\
5 & 7
\end{bmatrix}
-
\begin{bmatrix}
-5 & 2 \\
4 & 10
\end{bmatrix}
$$

Solution:
To subtract two matrices, we subtract their corresponding elements.

$$
\begin{bmatrix}
1 - (-5) & -6 - 2 \\
5 - 4 & 7 - 10
\end{bmatrix}
=
\begin{bmatrix}
1 + 5 & -6 - 2 \\
5 - 4 & 7 - 10
\end{bmatrix}
=
\begin{bmatrix}
6 & -8 \\
1 & -3
\end{bmatrix}
$$

Answer:
$$
\boxed{\begin{bmatrix}
6 & -8 \\
1 & -3
\end{bmatrix}}
$$

---

#### Problem 3:
$$
\begin{bmatrix}
17 & 8 & 0 \\
3 & -5 & 2
\end{bmatrix}
-
\begin{bmatrix}
4 & 6 & 5 \\
2 & -2 & 9
\end{bmatrix}
$$

Solution:
Subtract the corresponding elements of the matrices.

$$
\begin{bmatrix}
17 - 4 & 8 - 6 & 0 - 5 \\
3 - 2 & -5 - (-2) & 2 - 9
\end{bmatrix}
=
\begin{bmatrix}
13 & 2 & -5 \\
1 & -5 + 2 & 2 - 9
\end{bmatrix}
=
\begin{bmatrix}
13 & 2 & -5 \\
1 & -3 & -7
\end{bmatrix}
$$

Answer:
$$
\boxed{\begin{bmatrix}
13 & 2 & -5 \\
1 & -3 & -7
\end{bmatrix}}
$$

---

#### Problem 4:
$$
\begin{bmatrix}
-1 & 6 \\
5 & 2 \\
-5 & -1 \\
4 & -4
\end{bmatrix}
+
\begin{bmatrix}
-3 & 5 \\
4 & 1 \\
1 & -1 \\
4 & -4
\end{bmatrix}
$$

Solution:
Add the corresponding elements of the matrices.

$$
\begin{bmatrix}
-1 + (-3) & 6 + 5 \\
5 + 4 & 2 + 1 \\
-5 + 1 & -1 + (-1) \\
4 + 4 & -4 + (-4)
\end{bmatrix}
=
\begin{bmatrix}
-1 - 3 & 6 + 5 \\
5 + 4 & 2 + 1 \\
-5 + 1 & -1 - 1 \\
4 + 4 & -4 - 4
\end{bmatrix}
=
\begin{bmatrix}
-4 & 11 \\
9 & 3 \\
-4 & -2 \\
8 & -8
\end{bmatrix}
$$

Answer:
$$
\boxed{\begin{bmatrix}
-4 & 11 \\
9 & 3 \\
-4 & -2 \\
8 & -8
\end{bmatrix}}
$$

---

#### Problem 5:
$$
\begin{bmatrix}
-6 & -4 & -2 & -1
\end{bmatrix}
-
\begin{bmatrix}
5 & 5 & 4 & 2
\end{bmatrix}
-
\begin{bmatrix}
8 & -1 & -2 & 0
\end{bmatrix}
$$

Solution:
Subtract the corresponding elements step by step.

First, subtract the second matrix from the first:
$$
\begin{bmatrix}
-6 - 5 & -4 - 5 & -2 - 4 & -1 - 2
\end{bmatrix}
=
\begin{bmatrix}
-11 & -9 & -6 & -3
\end{bmatrix}
$$

Next, subtract the third matrix from the result:
$$
\begin{bmatrix}
-11 - 8 & -9 - (-1) & -6 - (-2) & -3 - 0
\end{bmatrix}
=
\begin{bmatrix}
-11 - 8 & -9 + 1 & -6 + 2 & -3 - 0
\end{bmatrix}
=
\begin{bmatrix}
-19 & -8 & -4 & -3
\end{bmatrix}
$$

Answer:
$$
\boxed{\begin{bmatrix}
-19 & -8 & -4 & -3
\end{bmatrix}}
$$

---

#### Problem 6:
$$
\begin{bmatrix}
3 & 5 & -7
\end{bmatrix}
+
\begin{bmatrix}
-4 & 6 & -1
\end{bmatrix}
$$

Solution:
Add the corresponding elements of the matrices.

$$
\begin{bmatrix}
3 + (-4) & 5 + 6 & -7 + (-1)
\end{bmatrix}
=
\begin{bmatrix}
3 - 4 & 5 + 6 & -7 - 1
\end{bmatrix}
=
\begin{bmatrix}
-1 & 11 & -8
\end{bmatrix}
$$

Answer:
$$
\boxed{\begin{bmatrix}
-1 & 11 & -8
\end{bmatrix}}
$$

---

#### Problem 7:
$$
\begin{bmatrix}
5 & -2 & -1 & -1 \\
-2 & -5 & 6 & 2
\end{bmatrix}
+
\begin{bmatrix}
-6 & 6 & -4 & 4 \\
0 & 0 & 1 & 2
\end{bmatrix}
$$

Solution:
Add the corresponding elements of the matrices.

$$
\begin{bmatrix}
5 + (-6) & -2 + 6 & -1 + (-4) & -1 + 4 \\
-2 + 0 & -5 + 0 & 6 + 1 & 2 + 2
\end{bmatrix}
=
\begin{bmatrix}
5 - 6 & -2 + 6 & -1 - 4 & -1 + 4 \\
-2 + 0 & -5 + 0 & 6 + 1 & 2 + 2
\end{bmatrix}
=
\begin{bmatrix}
-1 & 4 & -5 & 3 \\
-2 & -5 & 7 & 4
\end{bmatrix}
$$

Answer:
$$
\boxed{\begin{bmatrix}
-1 & 4 & -5 & 3 \\
-2 & -5 & 7 & 4
\end{bmatrix}}
$$

---

#### Problem 8:
$$
\begin{bmatrix}
5 & 2 \\
-5 & -1 \\
0 & 0 \\
4 & 3
\end{bmatrix}
+
\begin{bmatrix}
-2 & 5 \\
-5 & 1 \\
-6 & -6 \\
4 & -6
\end{bmatrix}
$$

Solution:
Add the corresponding elements of the matrices.

$$
\begin{bmatrix}
5 + (-2) & 2 + 5 \\
-5 + (-5) & -1 + 1 \\
0 + (-6) & 0 + (-6) \\
4 + 4 & 3 + (-6)
\end{bmatrix}
=
\begin{bmatrix}
5 - 2 & 2 + 5 \\
-5 - 5 & -1 + 1 \\
0 - 6 & 0 - 6 \\
4 + 4 & 3 - 6
\end{bmatrix}
=
\begin{bmatrix}
3 & 7 \\
-10 & 0 \\
-6 & -6 \\
8 & -3
\end{bmatrix}
$$

Answer:
$$
\boxed{\begin{bmatrix}
3 & 7 \\
-10 & 0 \\
-6 & -6 \\
8 & -3
\end{bmatrix}}
$$

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Final Answers:

1. $\boxed{\begin{bmatrix} 6 & 3 \\ -3 & 2 \end{bmatrix}}$
2. $\boxed{\begin{bmatrix} 6 & -8 \\ 1 & -3 \end{bmatrix}}$
3. $\boxed{\begin{bmatrix} 13 & 2 & -5 \\ 1 & -3 & -7 \end{bmatrix}}$
4. $\boxed{\begin{bmatrix} -4 & 11 \\ 9 & 3 \\ -4 & -2 \\ 8 & -8 \end{bmatrix}}$
5. $\boxed{\begin{bmatrix} -19 & -8 & -4 & -3 \end{bmatrix}}$
6. $\boxed{\begin{bmatrix} -1 & 11 & -8 \end{bmatrix}}$
7. $\boxed{\begin{bmatrix} -1 & 4 & -5 & 3 \\ -2 & -5 & 7 & 4 \end{bmatrix}}$
8. $\boxed{\begin{bmatrix} 3 & 7 \\ -10 & 0 \\ -6 & -6 \\ 8 & -3 \end{bmatrix}}$