https://file.aiquickdraw.com/mathbot/file/1727284878685ytgg8oge.jpg

The image shows a mathematical problem involving the scalar multiplication of a vector.

The problem is:
\[
\begin{pmatrix}
3 \\
2 \\
-1
\end{pmatrix} \cdot 2
\]

This involves multiplying each element of the vector by the scalar \( 2 \). Let's solve it:

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

So, the result is:
\[
\begin{pmatrix}
6 \\
4 \\
-2
\end{pmatrix}
\]

Would you like further details on this solution? Here are five related questions to deepen your understanding:

1. What is scalar multiplication in the context of vectors?
2. How does scalar multiplication differ from vector addition?
3. Can you generalize this for multiplying a vector by any scalar?
4. What is the geometric interpretation of scalar multiplication on vectors?
5. How does scalar multiplication apply in higher dimensions, such as in 4D or 5D vectors?

**Tip:** When multiplying a vector by a scalar, the magnitude of the vector changes by the scalar factor, but the direction remains the same unless the scalar is negative.

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

This problem involves multiplying a vector (3, 2, -1) by a scalar 2. Explore scalar multiplication in vector algebra with step-by-step solutions, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation