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The solution to the matrix equation \( AX = B \) is:

\[
X = \begin{bmatrix} -9 \\ 3 \\ 7 \end{bmatrix}
\]

Would you like a detailed explanation of the solution process or have any additional questions?

Here are 5 related questions to expand on this concept:
1. What is the determinant of matrix \( A \), and how does it affect the solution?
2. How would the solution change if matrix \( A \) were singular (non-invertible)?
3. Can you find the inverse of matrix \( A \), and how would it help solve \( AX = B \)?
4. What are some practical applications of solving matrix equations in real-world problems?
5. How can this method be extended to larger systems of equations?

**Tip:** In matrix equations, ensure the matrix \( A \) is non-singular (invertible) to guarantee a unique solution for \( X \).

Solve the matrix equation AX = B for X where A = [[7, 2, 0], [9, 3, -2], [-3, -1, 1]] and B = [[-57], [-86], [31]].

Learn how to solve the matrix equation AX = B, where A is a 3x3 matrix and B is a 3x1 matrix. This problem involves key linear algebra concepts, including matrix inversion and system of linear equations. Suitable for students studying linear algebra at the undergraduate level.

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