https://file.aiquickdraw.com/mathbot/file/17273192116621t4pbss0.jpg

The problem presented in the image involves multiplying a column vector by a scalar. The vector is:

\[
\begin{pmatrix}
2 \\
-1 \\
-3
\end{pmatrix}
\]
and it is being multiplied by the scalar 2.

To solve this, multiply each element of the vector by 2:

\[
2 \cdot \begin{pmatrix}
2 \\
-1 \\
-3
\end{pmatrix}
= \begin{pmatrix}
2 \times 2 \\
2 \times (-1) \\
2 \times (-3)
\end{pmatrix}
= \begin{pmatrix}
4 \\
-2 \\
-6
\end{pmatrix}
\]

So the result of the multiplication is:

\[
\begin{pmatrix}
4 \\
-2 \\
-6
\end{pmatrix}
\]

Let me know if you'd like more details or further explanation!

Here are 5 related questions:
1. What is the result of multiplying a 3x1 vector by a negative scalar?
2. How do you multiply a matrix by a scalar?
3. What is the geometric interpretation of scalar multiplication on a vector?
4. How do you add or subtract two column vectors?
5. Can scalar multiplication change the direction of a vector?

**Tip:** When multiplying vectors by scalars, only the magnitude is affected unless the scalar is negative, in which case the direction reverses.

Multiply the vector (2, -1, -3) by the scalar 2.

Learn how to perform scalar multiplication of a vector. This example shows the step-by-step solution for multiplying the vector (2, -1, -3) by the scalar 2, covering fundamental concepts in linear algebra and vector operations. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation