Math Problem Statement

Given the following matrices, if possible, determine 3A. If not, state 'Not possible'. A = [[-3, -7], [0, -1], [8, 6]]

Solution

To solve the problem of finding 3A3A, where the matrix AA is:

-3 & -7 \\ 0 & -1 \\ 8 & 6 \end{bmatrix}$$ You are tasked with multiplying the matrix by 3. Here's the process: ### Step-by-Step Solution: Multiply each element of the matrix by 3: $$3A = 3 \times \begin{bmatrix} -3 & -7 \\ 0 & -1 \\ 8 & 6 \end{bmatrix} = \begin{bmatrix} 3 \times (-3) & 3 \times (-7) \\ 3 \times 0 & 3 \times (-1) \\ 3 \times 8 & 3 \times 6 \end{bmatrix}$$ Now perform the multiplication: $$3A = \begin{bmatrix} -9 & -21 \\ 0 & -3 \\ 24 & 18 \end{bmatrix}$$ Thus, the matrix $$3A$$ is: $$3A = \begin{bmatrix} -9 & -21 \\ 0 & -3 \\ 24 & 18 \end{bmatrix}$$ Let me know if you'd like further clarification or details! --- Here are 5 related questions to explore this further: 1. What happens when you multiply a matrix by a negative scalar? 2. How do matrix addition and scalar multiplication differ? 3. What is the result if you multiply a matrix by 0? 4. How does scalar multiplication affect the determinant of a matrix? 5. Can scalar multiplication be applied to non-square matrices? **Tip:** When multiplying a matrix by a scalar, each element of the matrix is affected independently of the others.

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Math Problem Analysis

Mathematical Concepts

Matrix Multiplication
Scalar Multiplication

Formulas

Scalar Multiplication of a Matrix: cA = [[c * a11, c * a12], [c * a21, c * a22], ...]

Theorems

Properties of Scalar Multiplication in Matrices

Suitable Grade Level

Grades 10-12