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The problem involves multiplying a 1x3 matrix by a 3x1 matrix. Here's how you can solve it step-by-step:

### Problem:
\[
\begin{bmatrix} -2 & -1 & 3 \end{bmatrix} \cdot \begin{bmatrix} 3 \\ -2 \\ 2 \end{bmatrix}
\]

### Solution:
To perform this multiplication, you multiply corresponding elements and then sum them:

\[
(-2) \cdot 3 + (-1) \cdot (-2) + 3 \cdot 2
\]

Now, let's calculate each term:

1. \((-2) \cdot 3 = -6\)
2. \((-1) \cdot (-2) = 2\)
3. \(3 \cdot 2 = 6\)

Adding these results:

\[
-6 + 2 + 6 = 2
\]

### Final Answer:
\[
\begin{bmatrix} -2 & -1 & 3 \end{bmatrix} \cdot \begin{bmatrix} 3 \\ -2 \\ 2 \end{bmatrix} = 2
\]

Would you like more details or have any questions? 

Here are some related questions for further exploration:

1. How do you multiply matrices of different sizes?
2. What are the conditions for matrix multiplication to be possible?
3. How can matrix multiplication be used in solving systems of linear equations?
4. What is the significance of the dot product in vector operations?
5. How can matrix operations be used in computer graphics and transformations?

**Tip:** When multiplying matrices, always ensure that the number of columns in the first matrix equals the number of rows in the second matrix for the multiplication to be valid.

Multiply the 1x3 matrix [-2, -1, 3] by the 3x1 matrix [3, -2, 2].

Learn how to multiply a 1x3 matrix by a 3x1 matrix using dot product rules. This step-by-step solution walks you through the process, making it ideal for students in grades 9-12 studying matrix multiplication and linear algebra concepts.

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