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Let's analyze the problem to determine if the matrix operation \( A + B + C \) is possible.

### Step 1: Determine the Dimensions
First, let’s find the dimensions of each matrix.

- **Matrix A** is given as:
  \[
  A = \begin{bmatrix} -4 & -4 \\ 1 & -3 \\ -8 & 9 \end{bmatrix}
  \]
  Dimensions: \( 3 \times 2 \) (3 rows and 2 columns)

- **Matrix B** is given as:
  \[
  B = \begin{bmatrix} 1 & -3 \\ -5 & -4 \\ 4 & 3 \end{bmatrix}
  \]
  Dimensions: \( 3 \times 2 \) (3 rows and 2 columns)

- **Matrix C** is given as:
  \[
  C = \begin{bmatrix} -6 & -1 \\ -10 & -9 \\ -9 & -8 \end{bmatrix}
  \]
  Dimensions: \( 3 \times 2 \) (3 rows and 2 columns)

### Step 2: Check if Addition is Possible
For matrix addition to be possible, all matrices involved must have the same dimensions.

- Matrices **A**, **B**, and **C** all have dimensions of \( 3 \times 2 \).

Since they all have the same dimensions, addition is **possible**.

### Step 3: Perform the Addition
Now, we will add the corresponding elements from each matrix.

\[
A + B + C = \begin{bmatrix} -4 & -4 \\ 1 & -3 \\ -8 & 9 \end{bmatrix} + \begin{bmatrix} 1 & -3 \\ -5 & -4 \\ 4 & 3 \end{bmatrix} + \begin{bmatrix} -6 & -1 \\ -10 & -9 \\ -9 & -8 \end{bmatrix}
\]

Calculating each element:

1. First row:
   - \((-4 + 1 - 6) = -9\)
   - \((-4 + (-3) - 1) = -8\)

2. Second row:
   - \((1 + (-5) - 10) = -14\)
   - \((-3 + (-4) - 9) = -16\)

3. Third row:
   - \((-8 + 4 - 9) = -13\)
   - \((9 + 3 - 8) = 4\)

Thus:

\[
A + B + C = \begin{bmatrix} -9 & -8 \\ -14 & -16 \\ -13 & 4 \end{bmatrix}
\]

### Final Answer
\[
A + B + C = \begin{bmatrix} -9 & -8 \\ -14 & -16 \\ -13 & 4 \end{bmatrix}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you determine if two matrices can be multiplied?
2. What are the properties of matrix addition?
3. How can you find the transpose of a matrix?
4. How do you perform scalar multiplication with matrices?
5. What is the identity matrix and how is it used?

### Tip:
Always make sure that the matrices involved in addition have the exact same dimensions before attempting to add them.

Given the following matrices, if possible, determine A + B + C. If not, state 'Not Possible'. Matrices: A = [[-4, -4], [1, -3], [-8, 9]], B = [[1, -3], [-5, -4], [4, 3]], C = [[-6, -1], [-10, -9], [-9, -8]].

Determine the sum of three 3x2 matrices, A, B, and C. This problem involves checking matrix dimensions and performing element-wise addition. Suitable for students in Grades 10-12 learning linear algebra and matrix operations.

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