Math Problem Statement
Multiply the vector (2, -1, -3) by the scalar 2.
Solution
The problem presented in the image involves multiplying a column vector by a scalar. The vector is:
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.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Vector Scalar Multiplication
Linear Algebra
Formulas
v * k = (k*v1, k*v2, k*v3)
Theorems
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Suitable Grade Level
Grades 9-12