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The question asks to multiply the scalar \( 4 \) by the vector:

\[
\begin{bmatrix}
-1 \\
5 \\
4 \\
3
\end{bmatrix}
\]

To solve this, we multiply each element of the vector by 4:

\[
4 \times \begin{bmatrix} -1 \\ 5 \\ 4 \\ 3 \end{bmatrix} = \begin{bmatrix} 4 \times (-1) \\ 4 \times 5 \\ 4 \times 4 \\ 4 \times 3 \end{bmatrix} = \begin{bmatrix} -4 \\ 20 \\ 16 \\ 12 \end{bmatrix}
\]

Thus, the result is:

\[
\begin{bmatrix} -4 \\ 20 \\ 16 \\ 12 \end{bmatrix}
\]

The correct answer is the third option.

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. What is the result of multiplying \( 3 \) by the vector \( \begin{bmatrix} 2 \\ -3 \\ 0 \\ 5 \end{bmatrix} \)?
2. How do you multiply a scalar by a matrix?
3. What is a scalar, and how does it differ from a vector?
4. How can you check if the scalar multiplication of a matrix is correct?
5. What is the geometric interpretation of scalar multiplication of a vector?

**Tip**: When multiplying a scalar by a vector, always ensure each component of the vector is multiplied individually by the scalar.

What is 4 times the vector [-1, 5, 4, 3]?

Learn how to multiply the scalar 4 by the vector [-1, 5, 4, 3] using simple scalar multiplication rules. A step-by-step solution is provided to guide students in Grades 9-12.

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