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We are given two matrices \( M \) and \( N \):

\[
M = \begin{bmatrix} 
2 & 4 & 6 \\ 
5 & 10 & 15 \\ 
3 & 6 & 9 
\end{bmatrix}, \quad N = \begin{bmatrix} 
-1 & 0 & -3 \\ 
2 & 9 & 12 \\ 
7 & -10 & 11 
\end{bmatrix}
\]

We are tasked with calculating \( 2M + N \).

### Step 1: Compute \( 2M \)
Multiply each element of matrix \( M \) by 2:
\[
2M = 2 \times \begin{bmatrix} 
2 & 4 & 6 \\ 
5 & 10 & 15 \\ 
3 & 6 & 9 
\end{bmatrix} 
= \begin{bmatrix} 
4 & 8 & 12 \\ 
10 & 20 & 30 \\ 
6 & 12 & 18 
\end{bmatrix}
\]

### Step 2: Compute \( 2M + N \)
Now, we add matrices \( 2M \) and \( N \) element-wise:
\[
2M + N = \begin{bmatrix} 
4 & 8 & 12 \\ 
10 & 20 & 30 \\ 
6 & 12 & 18 
\end{bmatrix} 
+ \begin{bmatrix} 
-1 & 0 & -3 \\ 
2 & 9 & 12 \\ 
7 & -10 & 11 
\end{bmatrix}
= \begin{bmatrix} 
4 + (-1) & 8 + 0 & 12 + (-3) \\ 
10 + 2 & 20 + 9 & 30 + 12 \\ 
6 + 7 & 12 + (-10) & 18 + 11 
\end{bmatrix}
\]

\[
= \begin{bmatrix} 
3 & 8 & 9 \\ 
12 & 29 & 42 \\ 
13 & 2 & 29 
\end{bmatrix}
\]

Thus, the value of \( 2M + N \) is:
\[
\boxed{\begin{bmatrix} 
3 & 8 & 9 \\ 
12 & 29 & 42 \\ 
13 & 2 & 29 
\end{bmatrix}}
\]

Would you like more details on this process or have any questions?

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Here are five questions to expand on this:

1. How do you multiply a matrix by a scalar?
2. What are the properties of matrix addition?
3. Can we always add two matrices of different sizes?
4. How is matrix multiplication different from matrix addition?
5. What are some real-world applications of matrices?

**Tip:** Always ensure matrices are of the same dimensions before adding or subtracting them.

Diketahui matriks M = [2, 4, 6; 5, 10, 15; 3, 6, 9] dan matriks N = [-1, 0, -3; 2, 9, 12; 7, -10, 11]. Berapakah nilai 2M + N?

Learn how to solve a matrix operation problem involving scalar multiplication and matrix addition. This problem includes two matrices M and N and asks for the result of 2M + N. Suitable for students in Grades 10-12.

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