Let's analyze and solve the problem provided in the image:

Given:

• Matrix $A = \begin{bmatrix} 3 & -2 \\ 4 & -1 \end{bmatrix}$
• Matrix $B = \begin{bmatrix} 4 & 3 \\ -2 & -1 \end{bmatrix}$
• Matrix $C = \begin{bmatrix} 4 & 9 \\ 10 & 12 \end{bmatrix}$

We need to calculate: $(C - A) + (C - B)$

Step 1: Calculate $C - A$

$C - A = \begin{bmatrix} 4 & 9 \\ 10 & 12 \end{bmatrix} - \begin{bmatrix} 3 & -2 \\ 4 & -1 \end{bmatrix} = \begin{bmatrix} 4 - 3 & 9 - (-2) \\ 10 - 4 & 12 - (-1) \end{bmatrix} = \begin{bmatrix} 1 & 11 \\ 6 & 13 \end{bmatrix}$

Step 2: Calculate $C - B$

$C - B = \begin{bmatrix} 4 & 9 \\ 10 & 12 \end{bmatrix} - \begin{bmatrix} 4 & 3 \\ -2 & -1 \end{bmatrix} = \begin{bmatrix} 4 - 4 & 9 - 3 \\ 10 - (-2) & 12 - (-1) \end{bmatrix} = \begin{bmatrix} 0 & 6 \\ 12 & 13 \end{bmatrix}$

Step 3: Add the results

$(C - A) + (C - B) = \begin{bmatrix} 1 & 11 \\ 6 & 13 \end{bmatrix} + \begin{bmatrix} 0 & 6 \\ 12 & 13 \end{bmatrix} = \begin{bmatrix} 1 & 17 \\ 18 & 26 \end{bmatrix}$

However, the given options in the problem do not contain this result directly, indicating a possible mistake in either problem formulation or the provided options.

Would you like a more detailed explanation, or do you have any questions about the steps?

Here are 5 related questions to deepen your understanding:

1. How do you subtract two matrices with different dimensions?
2. What is the general formula for adding matrices?
3. How do matrix operations differ from scalar operations?
4. What are some applications of matrix addition in real-world problems?
5. How does matrix subtraction affect the determinants of the resulting matrices?

Tip: When working with matrices, ensure that dimensions match before performing operations like addition or subtraction.