Math Problem Statement
The augmented matrix below represents a system of equations. Which matrix results from the operation R1 ↔ R2?
Solution
To solve this problem, the operation means swapping the first row () with the second row () in the given augmented matrix.
Original matrix:
-1 & 1 & 2 & 7 \\ -3 & 2 & 1 & 4 \\ 2 & 1 & 1 & 7 \end{bmatrix}$$ ### Perform $$R_1 \leftrightarrow R_2$$: After swapping $$R_1$$ and $$R_2$$, the matrix becomes: $$\begin{bmatrix} -3 & 2 & 1 & 4 \\ -1 & 1 & 2 & 7 \\ 2 & 1 & 1 & 7 \end{bmatrix}$$ ### Result: The resulting matrix after the operation $$R_1 \leftrightarrow R_2$$ is: $$\begin{bmatrix} -3 & 2 & 1 & 4 \\ -1 & 1 & 2 & 7 \\ 2 & 1 & 1 & 7 \end{bmatrix}$$ Let me know if you need further clarification or want additional operations explained. --- Here are 5 related questions to expand your understanding: 1. What does the operation $$R_1 \leftrightarrow R_3$$ result in for the given matrix? 2. What are row operations, and how are they used to solve a system of equations? 3. How would you reduce the given matrix to row echelon form? 4. What does performing $$R_2 \rightarrow R_2 + 3R_1$$ result in for this matrix? 5. How can augmented matrices represent systems of linear equations? **Tip:** Swapping rows in an augmented matrix is often used to simplify further row operations or improve computational efficiency when solving linear systems.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Row Operations
Matrix Representation of Linear Systems
Formulas
Swapping Rows: R1 ↔ R2
Theorems
Elementary Row Operations
Suitable Grade Level
Grades 10-12