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The image shows a problem related to matrix algebra. From the image, we can extract the following information:

- You have a system of linear equations given in matrix form as \( AX = B \).
- The matrix \( A \) is a \( 3 \times 3 \) matrix, which is given as:
\[
A = \begin{pmatrix}
1 & 1 & -2 \\
1 & -1 & 3 \\
2 & -2 & 1
\end{pmatrix}
\]
- The matrix \( B \) is a \( 3 \times 1 \) column matrix, given as:
\[
B = \begin{pmatrix}
-5 \\
4 \\
9
\end{pmatrix}
\]

The problem requires finding the matrix \( X \), which satisfies the equation \( AX = B \).

### Solution Steps:

1. **Matrix Form of the Equation**:
   The equation is \( AX = B \), where \( A \) is a \( 3 \times 3 \) matrix, \( X \) is a \( 3 \times 1 \) column matrix (which we need to find), and \( B \) is a \( 3 \times 1 \) column matrix.

2. **Inverse of Matrix \( A \)**:
   To find \( X \), you need to multiply both sides of the equation by the inverse of \( A \):
   \[
   X = A^{-1}B
   \]
   First, we need to calculate the inverse \( A^{-1} \) of matrix \( A \).

3. **Calculate the Inverse \( A^{-1} \)**:
   The inverse of a \( 3 \times 3 \) matrix \( A \) can be calculated using the formula:
   \[
   A^{-1} = \frac{1}{\

Learn how to solve a matrix equation AX = B using the inverse of a 3x3 matrix. This example problem involves finding the matrix X that satisfies the equation given matrices A and B. Suitable for advanced high school or college-level students.

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