https://file.aiquickdraw.com/mathbot/file/17274633977995nrrsmiy.jpg

The image shows a scalar multiplication of a matrix. The scalar is \(\frac{1}{-3}\), and it is being multiplied by a \(3 \times 3\) matrix:

\[
\begin{bmatrix}
-6 & 12 & -3 \\
7 & -12 & 2 \\
-3 & 3 & 0
\end{bmatrix}
\]

To perform scalar multiplication, we multiply each element of the matrix by \(\frac{1}{-3}\).

Let's compute the result step by step:

1. Multiply \(-6\) by \(\frac{1}{-3}\): \(\frac{-6}{-3} = 2\)
2. Multiply \(12\) by \(\frac{1}{-3}\): \(\frac{12}{-3} = -4\)
3. Multiply \(-3\) by \(\frac{1}{-3}\): \(\frac{-3}{-3} = 1\)
4. Multiply \(7\) by \(\frac{1}{-3}\): \(\frac{7}{-3} = -\frac{7}{3}\)
5. Multiply \(-12\) by \(\frac{1}{-3}\): \(\frac{-12}{-3} = 4\)
6. Multiply \(2\) by \(\frac{1}{-3}\): \(\frac{2}{-3} = -\frac{2}{3}\)
7. Multiply \(-3\) by \(\frac{1}{-3}\): \(\frac{-3}{-3} = 1\)
8. Multiply \(3\) by \(\frac{1}{-3}\): \(\frac{3}{-3} = -1\)
9. Multiply \(0\) by \(\frac{1}{-3}\): \(0 \times \frac{1}{-3} = 0\)

The resulting matrix after multiplication is:

\[
\begin{bmatrix}
2 & -4 & 1 \\
-\frac{7}{3} & 4 & -\frac{2}{3} \\
1 & -1 & 0
\end{bmatrix}
\]

Would you like further details or explanations on any part of this?

Here are some related questions:
1. How do you find the determinant of a \(3 \times 3\) matrix?
2. What are the properties of scalar multiplication in matrices?
3. How do matrix transformations affect geometric shapes?
4. What is the inverse of a matrix and how is it related to determinants?
5. How do you multiply two matrices together?

**Tip**: When multiplying matrices by a scalar, remember each element gets multiplied independently of the others.

Multiply the matrix by the scalar \( \frac{1}{-3} \) and find the resulting matrix.

Learn how to perform matrix scalar multiplication by multiplying a 3x3 matrix by a scalar of 1/-3. Follow the detailed steps to find the resulting matrix, covering key concepts in linear algebra and scalar operations.

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