Math Problem Statement
Perform the row operation 7R1 → R1 on the following matrix:
[ 1 -3 2 ]
[ 4 -6 -8 ]
Solution
The given matrix is:
1 & -3 & 2 \\ 4 & -6 & -8 \end{bmatrix}$$ You are asked to perform the row operation $$7R_1 \rightarrow R_1$$. This means that you need to multiply the first row $$R_1$$ by 7 and place the result back into the first row. Let's proceed step-by-step: 1. Multiply each element in the first row by 7: - The first element $$1 \times 7 = 7$$ - The second element $$-3 \times 7 = -21$$ - The third element $$2 \times 7 = 14$$ So, the new matrix after applying the row operation is: $$\begin{bmatrix} 7 & -21 & 14 \\ 4 & -6 & -8 \end{bmatrix}$$ Would you like more details or have any further questions on this? Here are some related questions: 1. How do you perform other types of row operations in matrix transformations? 2. What are the types of elementary row operations? 3. Can row operations be used to solve systems of linear equations? 4. How does performing a row operation affect the determinant of a matrix? 5. What are the applications of row operations in matrix theory? **Tip:** When performing row operations, it's crucial to maintain the integrity of the matrix's structure to ensure accurate results, especially when solving linear equations.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Matrix Operations
Row Operations
Elementary Row Transformations
Formulas
R1 → 7R1 (Multiply each element in R1 by 7)
Theorems
Elementary Row Operation Theorem
Suitable Grade Level
Grades 9-12