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Jse the specified row transformation to change the given matrix. 145 7R, + R2 -7 2 -1 9 7 ..... What is the transformed matrix? 4 5 9 7 0 .....

Jse the specified row transformation to change the given matrix. 145 7R, + R2 -7 2 -1 9 7 ..... What is the transformed matrix? 4 5 9 7 0 .....

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Row Transformation of a Matrix #### Task Use the specified row transformation to change the given matrix using the operation \(7R_1 + R_2\). #### Given Matrix \[ \begin{bmatrix} 1 & 4 & 5 \\ -7 & 2 & -1 \\ 9 & 7 & 0 \end{bmatrix} \] #### Row Transformation - Apply the transformation \(7R_1 + R_2\) to the matrix. #### Matrix Operation 1. **Identify Rows**: - \(R_1\) = [1, 4, 5] - \(R_2\) = [-7, 2, -1] - \(R_3\) = [9, 7, 0] 2. **Perform the Operation**: - Replace \(R_2\) with the result of \(7R_1 + R_2\). - Calculate \(7R_1\): \[ 7 \times R_1 = [7 \times 1, 7 \times 4, 7 \times 5] = [7, 28, 35] \] - Add this to \(R_2\): \[ [7, 28, 35] + [-7, 2, -1] = [0, 30, 34] \] 3. **Resulting Matrix**: \[ \begin{bmatrix} 1 & 4 & 5 \\ 0 & 30 & 34 \\ 9 & 7 & 0 \end{bmatrix} \] ### Conclusion The matrix after applying the transformation \(7R_1 + R_2\) to \(R_2\) is: \[ \begin{bmatrix} 1 & 4 & 5 \\ 0 & 30 & 34 \\ 9 & 7 & 0 \end{bmatrix} \]
Transcribed Image Text:### Row Transformation of a Matrix #### Task Use the specified row transformation to change the given matrix using the operation \(7R_1 + R_2\). #### Given Matrix \[ \begin{bmatrix} 1 & 4 & 5 \\ -7 & 2 & -1 \\ 9 & 7 & 0 \end{bmatrix} \] #### Row Transformation - Apply the transformation \(7R_1 + R_2\) to the matrix. #### Matrix Operation 1. **Identify Rows**: - \(R_1\) = [1, 4, 5] - \(R_2\) = [-7, 2, -1] - \(R_3\) = [9, 7, 0] 2. **Perform the Operation**: - Replace \(R_2\) with the result of \(7R_1 + R_2\). - Calculate \(7R_1\): \[ 7 \times R_1 = [7 \times 1, 7 \times 4, 7 \times 5] = [7, 28, 35] \] - Add this to \(R_2\): \[ [7, 28, 35] + [-7, 2, -1] = [0, 30, 34] \] 3. **Resulting Matrix**: \[ \begin{bmatrix} 1 & 4 & 5 \\ 0 & 30 & 34 \\ 9 & 7 & 0 \end{bmatrix} \] ### Conclusion The matrix after applying the transformation \(7R_1 + R_2\) to \(R_2\) is: \[ \begin{bmatrix} 1 & 4 & 5 \\ 0 & 30 & 34 \\ 9 & 7 & 0 \end{bmatrix} \]
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