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D. Determine the solution for the following augmented matrix for a 3x3 linear system of equations. y r3 -9 18 (x, y, z) = (_) 7 | 14]

D. Determine the solution for the following augmented matrix for a 3x3 linear system of equations. y r3 -9 18 (x, y, z) = (_) 7 | 14]

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6). Determine the solution for the following augmented matrix for a 3x3 linear system of equations. \[ \begin{bmatrix} 3 & 0 & 0 & | & 6 \\ 0 & -9 & 0 & | & 18 \\ 0 & 0 & 7 & | & 14 \\ \end{bmatrix} \] \((x, y, z) = (\_\_, \_\_, \_\_)\) ### Explanation of the Augmented Matrix - This matrix represents a system of linear equations with three variables \(x\), \(y\), and \(z\). - The first column corresponds to the coefficients of \(x\), the second to \(y\), and the third to \(z\). - The numbers to the right of the vertical line represent the constants on the right side of each equation. ### System of Equations From the augmented matrix, the system of equations is: 1. \(3x = 6\) 2. \(-9y = 18\) 3. \(7z = 14\) ### Solving the System Solve each equation: 1. \(3x = 6\) \\ Divide both sides by 3: \\ \(x = 2\) 2. \(-9y = 18\) \\ Divide both sides by -9: \\ \(y = -2\) 3. \(7z = 14\) \\ Divide both sides by 7: \\ \(z = 2\) ### Solution The solution to the system of equations is: \((x, y, z) = (2, -2, 2)\)
Transcribed Image Text:6). Determine the solution for the following augmented matrix for a 3x3 linear system of equations. \[ \begin{bmatrix} 3 & 0 & 0 & | & 6 \\ 0 & -9 & 0 & | & 18 \\ 0 & 0 & 7 & | & 14 \\ \end{bmatrix} \] \((x, y, z) = (\_\_, \_\_, \_\_)\) ### Explanation of the Augmented Matrix - This matrix represents a system of linear equations with three variables \(x\), \(y\), and \(z\). - The first column corresponds to the coefficients of \(x\), the second to \(y\), and the third to \(z\). - The numbers to the right of the vertical line represent the constants on the right side of each equation. ### System of Equations From the augmented matrix, the system of equations is: 1. \(3x = 6\) 2. \(-9y = 18\) 3. \(7z = 14\) ### Solving the System Solve each equation: 1. \(3x = 6\) \\ Divide both sides by 3: \\ \(x = 2\) 2. \(-9y = 18\) \\ Divide both sides by -9: \\ \(y = -2\) 3. \(7z = 14\) \\ Divide both sides by 7: \\ \(z = 2\) ### Solution The solution to the system of equations is: \((x, y, z) = (2, -2, 2)\)
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