Math Problem Statement
Multiply the vector (3, 2, -1) by the scalar 2.
Solution
The image shows a mathematical problem involving the scalar multiplication of a vector.
The problem is:
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.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Vector Algebra
Scalar Multiplication
Formulas
Scalar Multiplication: k * (a, b, c) = (k*a, k*b, k*c)
Theorems
Scalar Multiplication of Vectors
Suitable Grade Level
Grades 8-10