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The matrix \( M \) is:

\[
M = \begin{bmatrix} 0 & 6 \\ 8 & -26 \end{bmatrix}
\]

Would you like a detailed explanation on how this was derived, or do you have any questions?

Here are some related questions:
1. What would change if the equation were \( A + M = 2B + C \)?
2. How do you solve matrix equations in general?
3. What happens if you replace \( C \) with a zero matrix in this equation?
4. Can you explain how matrix multiplication affects the dimensionality of the result?
5. How would you solve a system of linear equations using matrices?

**Tip:** When solving matrix equations, always ensure that the matrices involved are conformable for operations like addition, subtraction, or multiplication.

Given the matrices A = [[2, 3], [-3, 5]], B = [[-2, 3], [7, -18]], and C = [[6, 9], [-1, -11]], solve for M in the equation A + 2M = 2B + C.

Solve for the matrix M given the matrices A, B, and C in the equation A + 2M = 2B + C. This problem involves key concepts such as matrix addition and scalar multiplication, ideal for students in Grades 10-12.

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