Math Problem Statement

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

Solution

The question asks to multiply the scalar 44 by the vector:

-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.

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Math Problem Analysis

Mathematical Concepts

Scalar Multiplication
Vectors

Formulas

c * [a, b, c, d] = [c * a, c * b, c * c, c * d]

Theorems

Basic Properties of Scalar Multiplication

Suitable Grade Level

Grades 9-12