https://file.aiquickdraw.com/mathbot/file/17297389268276ku957oj.jpg

The image contains two matrix addition problems.

### First matrix addition:
\[
\begin{pmatrix}
3 & 5 & 6 & 7 \\
4 & 8 & 7 & 6
\end{pmatrix}
+
\begin{pmatrix}
3 & 6 & 2 & 4 \\
4 & 3 & 5 & 6
\end{pmatrix}
\]

### Solution:
\[
\begin{pmatrix}
3+3 & 5+6 & 6+2 & 7+4 \\
4+4 & 8+3 & 7+5 & 6+6
\end{pmatrix}
=
\begin{pmatrix}
6 & 11 & 8 & 11 \\
8 & 11 & 12 & 12
\end{pmatrix}
\]

### Second matrix addition:
\[
\begin{pmatrix}
3 & 5 & 6 & 7 \\
8 & 9 & 4 & 3 \\
2 & 3 & 9 & 5
\end{pmatrix}
+
\begin{pmatrix}
3 & 5 & 6 & 7 \\
\frac{1}{2} & 8 & 7 & 6 \\
\frac{1}{2} & 3 & \frac{1}{2} & 5
\end{pmatrix}
\]

### Solution:
\[
\begin{pmatrix}
3+3 & 5+5 & 6+6 & 7+7 \\
8+\frac{1}{2} & 9+8 & 4+7 & 3+6 \\
2+\frac{1}{2} & 3+3 & 9+\frac{1}{2} & 5+5
\end{pmatrix}
=
\begin{pmatrix}
6 & 10 & 12 & 14 \\
8.5 & 17 & 11 & 9 \\
2.5 & 6 & 9.5 & 10
\end{pmatrix}
\]

Would you like a deeper explanation of the steps? Here are five related questions to explore further:

1. How do you determine if two matrices can be added?
2. Can matrix addition be performed on matrices of different dimensions?
3. How does scalar multiplication differ from matrix addition?
4. What are some real-world applications of matrix operations?
5. What happens if you add a zero matrix to any matrix?

**Tip:** When adding matrices, ensure that both matrices have the same dimensions, otherwise, addition is not possible.

Solve matrix addition problems involving 2x2 and 3x4 matrices. Learn key matrix addition formulas and apply theorems for matrices of the same dimensions. Suitable for students in Grades 9-12.

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