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We are asked to determine the sum of the given expression, which involves scalar multiplication and vector addition. The expression is:

\[
0 \cdot \begin{pmatrix} -5 \\ 5 \\ 0 \end{pmatrix} + (-4) \cdot \begin{pmatrix} -2 \\ -2 \\ 3 \end{pmatrix}
\]

### Step 1: Multiply the scalars by the vectors.

1. Multiply the first vector by \( 0 \):

\[
0 \cdot \begin{pmatrix} -5 \\ 5 \\ 0 \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix}
\]

2. Multiply the second vector by \( -4 \):

\[
-4 \cdot \begin{pmatrix} -2 \\ -2 \\ 3 \end{pmatrix} = \begin{pmatrix} (-4) \cdot (-2) \\ (-4) \cdot (-2) \\ (-4) \cdot 3 \end{pmatrix} = \begin{pmatrix} 8 \\ 8 \\ -12 \end{pmatrix}
\]

### Step 2: Add the resulting vectors.

\[
\begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix} + \begin{pmatrix} 8 \\ 8 \\ -12 \end{pmatrix} = \begin{pmatrix} 8 \\ 8 \\ -12 \end{pmatrix}
\]

### Final Answer:
\[
\begin{pmatrix} 8 \\ 8 \\ -12 \end{pmatrix}
\]

Would you like any more details or further explanation?

Here are five related questions to deepen your understanding:
1. How do you compute the dot product of two vectors?
2. What is the difference between vector addition and scalar multiplication?
3. What is a zero vector, and how does it affect vector operations?
4. How do vectors relate to linear transformations in matrices?
5. How does scalar multiplication affect the direction and magnitude of a vector?

**Tip:** When performing vector operations, always handle scalar multiplication before adding the vectors.

Determine the sum: 0 * (-5, 5, 0) + (-4) * (-2, -2, 3)

Learn how to determine the sum of two vectors where one is multiplied by a scalar. This problem involves vector scalar multiplication and vector addition. Detailed step-by-step solution provided. Suitable for students in Grades 9-12.

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