Adding and Subtracting Matrices worksheet with six problems for simplifying matrix operations.

To solve the given problems involving matrix addition and subtraction, we need to follow these steps:

Matrix Addition

- Add corresponding elements of the matrices.
- The matrices must have the same dimensions.

Matrix Subtraction

- Subtract corresponding elements of the matrices.
- The matrices must have the same dimensions.

Let's solve each problem step by step.

---

Problem 1:

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

#### Step-by-Step Solution:
1. Add the corresponding elements:
- First row, first column: $-2 + (-2) = -4$
- First row, second column: $2 + 6 = 8$
- First row, third column: $3 + 3 = 6$
- Second row, first column: $-1 + 2 = 1$
- Second row, second column: $4 + 3 = 7$
- Second row, third column: $5 + 4 = 9$

2. Write the resulting matrix:
$$
\begin{bmatrix}
-4 & 8 & 6 \\
1 & 7 & 9
\end{bmatrix}
$$

#### Final Answer:
$$
\boxed{\begin{bmatrix}
-4 & 8 & 6 \\
1 & 7 & 9
\end{bmatrix}}
$$

---

Problem 2:

$$
\begin{bmatrix}
-1 & -2 \\
6 & 2 \\
8 & 5 \\
9 & 4
\end{bmatrix}
-
\begin{bmatrix}
-1 & 2 \\
4 & 2 \\
1 & 3 \\
4 & 2
\end{bmatrix}
$$

#### Step-by-Step Solution:
1. Subtract the corresponding elements:
- First row, first column: $-1 - (-1) = 0$
- First row, second column: $-2 - 2 = -4$
- Second row, first column: $6 - 4 = 2$
- Second row, second column: $2 - 2 = 0$
- Third row, first column: $8 - 1 = 7$
- Third row, second column: $5 - 3 = 2$
- Fourth row, first column: $9 - 4 = 5$
- Fourth row, second column: $4 - 2 = 2$

2. Write the resulting matrix:
$$
\begin{bmatrix}
0 & -4 \\
2 & 0 \\
7 & 2 \\
5 & 2
\end{bmatrix}
$$

#### Final Answer:
$$
\boxed{\begin{bmatrix}
0 & -4 \\
2 & 0 \\
7 & 2 \\
5 & 2
\end{bmatrix}}
$$

---

Problem 3:

$$
\begin{bmatrix}
6 & 3 & 1
\end{bmatrix}
+
\begin{bmatrix}
4 & 5 & 2
\end{bmatrix}
$$

#### Step-by-Step Solution:
1. Add the corresponding elements:
- First element: $6 + 4 = 10$
- Second element: $3 + 5 = 8$
- Third element: $1 + 2 = 3$

2. Write the resulting matrix:
$$
\begin{bmatrix}
10 & 8 & 3
\end{bmatrix}
$$

#### Final Answer:
$$
\boxed{\begin{bmatrix}
10 & 8 & 3
\end{bmatrix}}
$$

---

Problem 4:

$$
\begin{bmatrix}
-1 & 2 & 0 \\
-5 & 8 & 9
\end{bmatrix}
-
\begin{bmatrix}
-1 & 3 & -8 \\
1 & 4 & 7
\end{bmatrix}
$$

#### Step-by-Step Solution:
1. Subtract the corresponding elements:
- First row, first column: $-1 - (-1) = 0$
- First row, second column: $2 - 3 = -1$
- First row, third column: $0 - (-8) = 8$
- Second row, first column: $-5 - 1 = -6$
- Second row, second column: $8 - 4 = 4$
- Second row, third column: $9 - 7 = 2$

2. Write the resulting matrix:
$$
\begin{bmatrix}
0 & -1 & 8 \\
-6 & 4 & 2
\end{bmatrix}
$$

#### Final Answer:
$$
\boxed{\begin{bmatrix}
0 & -1 & 8 \\
-6 & 4 & 2
\end{bmatrix}}
$$

---

Problem 5:

$$
\begin{bmatrix}
-2 \\
4 \\
3 \\
1
\end{bmatrix}
-
\begin{bmatrix}
-6 \\
4 \\
1 \\
5
\end{bmatrix}
$$

#### Step-by-Step Solution:
1. Subtract the corresponding elements:
- First element: $-2 - (-6) = 4$
- Second element: $4 - 4 = 0$
- Third element: $3 - 1 = 2$
- Fourth element: $1 - 5 = -4$

2. Write the resulting matrix:
$$
\begin{bmatrix}
4 \\
0 \\
2 \\
-4
\end{bmatrix}
$$

#### Final Answer:
$$
\boxed{\begin{bmatrix}
4 \\
0 \\
2 \\
-4
\end{bmatrix}}
$$

---

Problem 6:

$$
\begin{bmatrix}
8 & 9 \\
-6 & -5 \\
2 & 4
\end{bmatrix}
-
\begin{bmatrix}
4 & -5 \\
4 & -4 \\
-6 & -5
\end{bmatrix}
$$

#### Step-by-Step Solution:
1. Subtract the corresponding elements:
- First row, first column: $8 - 4 = 4$
- First row, second column: $9 - (-5) = 14$
- Second row, first column: $-6 - 4 = -10$
- Second row, second column: $-5 - (-4) = -1$
- Third row, first column: $2 - (-6) = 8$
- Third row, second column: $4 - (-5) = 9$

2. Write the resulting matrix:
$$
\begin{bmatrix}
4 & 14 \\
-10 & -1 \\
8 & 9
\end{bmatrix}
$$

#### Final Answer:
$$
\boxed{\begin{bmatrix}
4 & 14 \\
-10 & -1 \\
8 & 9
\end{bmatrix}}
$$

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Summary of Answers:

1. $\boxed{\begin{bmatrix}
-4 & 8 & 6 \\
1 & 7 & 9
\end{bmatrix}}$
2. $\boxed{\begin{bmatrix}
0 & -4 \\
2 & 0 \\
7 & 2 \\
5 & 2
\end{bmatrix}}$
3. $\boxed{\begin{bmatrix}
10 & 8 & 3
\end{bmatrix}}$
4. $\boxed{\begin{bmatrix}
0 & -1 & 8 \\
-6 & 4 & 2
\end{bmatrix}}$
5. $\boxed{\begin{bmatrix}
4 \\
0 \\
2 \\
-4
\end{bmatrix}}$
6. $\boxed{\begin{bmatrix}
4 & 14 \\
-10 & -1 \\
8 & 9
\end{bmatrix}}$