Math Problem Statement
What is the result of multiplying a scalar 5 with the given 2x3 matrix: [[-4, 3, -2], [6, -1, 0]]?
Solution
The question involves multiplying a scalar (5) with a given matrix:
-4 & 3 & -2 \\ 6 & -1 & 0 \end{bmatrix}$$ We will perform the scalar multiplication: Each element of the matrix is multiplied by 5: $$5 \cdot \begin{bmatrix} -4 & 3 & -2 \\ 6 & -1 & 0 \end{bmatrix} = \begin{bmatrix} 5(-4) & 5(3) & 5(-2) \\ 5(6) & 5(-1) & 5(0) \end{bmatrix}$$ Performing the calculations: $$\begin{bmatrix} -20 & 15 & -10 \\ 30 & -5 & 0 \end{bmatrix}$$ Thus, the correct answer is: **$$-20, 15, -10, 30, -5, 0$$**, which matches the option: $$\boxed{-20, 15, -10, 30, -5, 0}$$ --- Do you have any further questions or want a deeper explanation? Here are 5 follow-up questions for exploration: 1. What happens when you multiply a matrix by a negative scalar? 2. Can you explain the difference between scalar multiplication and matrix multiplication? 3. How would the answer change if the scalar were a fraction (e.g., $$\frac{1}{2}$$)? 4. How does this operation relate to transformations in geometry? 5. What are some real-world applications of scalar multiplication in matrices? **Tip**: Always double-check your calculations when dealing with scalars and matrices to avoid simple arithmetic mistakes!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Algebra
Scalar Multiplication
Formulas
Scalar multiplication: c * A = [[c * a11, c * a12, c * a13], [c * a21, c * a22, c * a23]]
Theorems
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Suitable Grade Level
Grades 7-9