https://file.aiquickdraw.com/mathbot/file/1727980229514zxv29tk6.jpg

Let's solve the given matrix addition problem.

We are given two matrices to add:

\[
\begin{bmatrix}
3 \\
5
\end{bmatrix}
+
\begin{bmatrix}
3 \\
-6
\end{bmatrix}
\]

To add these matrices, we simply add their corresponding elements:

\[
\begin{bmatrix}
3 + 3 \\
5 + (-6)
\end{bmatrix}
=
\begin{bmatrix}
6 \\
-1
\end{bmatrix}
\]

So, the result is:

\[
\begin{bmatrix}
6 \\
-1
\end{bmatrix}
\]

Now, let's compare this result with the answer choices:

- **A)** \(\begin{bmatrix} 6 \\ 1 \end{bmatrix}\)
- **B)** \(\begin{bmatrix} 6 \\ 11 \end{bmatrix}\)
- **C)** \(\begin{bmatrix} 9 \\ -1 \end{bmatrix}\)
- **D)** \(\begin{bmatrix} 6 \\ -1 \end{bmatrix}\)

The correct answer is **D**.

Would you like any further details or explanations?

Here are some related questions to practice:
1. How would you subtract two matrices instead of adding them?
2. Can you add matrices of different dimensions? Why or why not?
3. What happens if you multiply two matrices of compatible sizes?
4. How do you perform scalar multiplication on a matrix?
5. What is the identity matrix, and how is it used in matrix operations?

**Tip:** Always make sure that the matrices you are adding or subtracting have the same dimensions for the operations to be valid!

Learn how to solve a matrix addition problem with the matrices [3, 5] and [3, -6]. This step-by-step guide covers key linear algebra concepts and matrix operations, ideal for students in Grades 8-10.

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