https://file.aiquickdraw.com/mathbot/file/17310836164983mgx44iq.jpg

To solve this problem, we need to determine the value of the scalar \( R \) that satisfies the equation involving two matrices:

\[
R \begin{bmatrix} 2 & 3 \\ -1 & 6 \end{bmatrix} = \begin{bmatrix} -6 & -9 \\ 3 & -18 \end{bmatrix}
\]

This equation implies that each element in the matrix on the left, when multiplied by \( R \), should equal the corresponding element in the matrix on the right. We can set up equations based on corresponding elements and solve for \( R \).

Let's match elements:

1. From the top left element:
   \[
   R \cdot 2 = -6 \Rightarrow R = \frac{-6}{2} = -3
   \]

2. We can verify this value with other elements:
   - Top right element: \( R \cdot 3 = -9 \Rightarrow R = \frac{-9}{3} = -3 \)
   - Bottom left element: \( R \cdot (-1) = 3 \Rightarrow R = \frac{3}{-1} = -3 \)
   - Bottom right element: \( R \cdot 6 = -18 \Rightarrow R = \frac{-18}{6} = -3 \)

In all cases, \( R = -3 \).

### Conclusion:
The value of the scalar \( R \) is \( \boxed{-3} \).

Would you like further details on matrix scalar multiplication or any other related topic?

Here are some questions that may expand on this topic:
1. How does scalar multiplication work with matrices?
2. How can we verify matrix equations step-by-step?
3. What are other types of matrix operations, like addition and multiplication?
4. How do we solve for a scalar in more complex matrix equations?
5. What are the properties of scalar multiplication in matrices?

**Tip:** When solving for a scalar in a matrix equation, always check each element to ensure consistency across the entire matrix.

Determine the value of the scalar R such that R multiplied by the matrix [[2, 3], [-1, 6]] equals the matrix [[-6, -9], [3, -18]].

Learn how to solve a matrix equation involving scalar multiplication. This problem focuses on finding the value of the scalar R such that R times the matrix [[2, 3], [-1, 6]] results in the matrix [[-6, -9], [3, -18]]. Suitable for high school students studying algebra and matrix operations.

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