https://file.aiquickdraw.com/mathbot/file/1729721072760ya67n2c8.jpg

The problem in the image is asking to perform matrix subtraction between two given matrices.

Let's define the two matrices:
Matrix \( A \):
\[
\begin{bmatrix}
3 & -9 \\
2 & 6 \\
-2 & 4
\end{bmatrix}
\]
Matrix \( B \):
\[
\begin{bmatrix}
-5 & -6 \\
6 & 7 \\
-5 & -9
\end{bmatrix}
\]

The subtraction operation \( A - B \) is performed element by element. That is:
\[
(A - B)_{ij} = A_{ij} - B_{ij}
\]

Let's compute each element:

- Top-left: \( 3 - (-5) = 3 + 5 = 8 \)
- Top-right: \( -9 - (-6) = -9 + 6 = -3 \)
- Middle-left: \( 2 - 6 = -4 \)
- Middle-right: \( 6 - 7 = -1 \)
- Bottom-left: \( -2 - (-5) = -2 + 5 = 3 \)
- Bottom-right: \( 4 - (-9) = 4 + 9 = 13 \)

So the result of the matrix subtraction is:
\[
\begin{bmatrix}
8 & -3 \\
-4 & -1 \\
3 & 13
\end{bmatrix}
\]

This is the final matrix after performing the operation.

Would you like more details on any of these steps or have any other questions? Here are some related questions you can explore:
1. How is matrix addition and subtraction defined for different-sized matrices?
2. What are the properties of matrix operations?
3. Can matrix subtraction be applied in systems of equations?
4. How does scalar multiplication interact with matrix subtraction?
5. How are matrix operations applied in linear transformations?

**Tip:** Always ensure the matrices involved in addition or subtraction have the same dimensions!

Perform the matrix subtraction operation between two 3x2 matrices as shown in the image.

Learn how to subtract two 3x2 matrices step-by-step with a detailed solution. This matrix operation involves element-wise subtraction and helps in understanding the basics of linear algebra. Suitable for college-level or advanced high school students.

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