Answered: What is the sequence of operations…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.2: Guassian Elimination And Matrix Methods

Problem 86E

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Question

What is the sequence of operations which could be used (using gauss-jordan elimination) to solve this system.

7x-2y-4z=16

-3x+y+2z=-7

6x-2y-4z=14

Expert Solution

Step 1

Given system of equations is

7x-2y-4z=16

-3x+y+2z=-7

6x-2y-4z=14

Associated augmented matrix is

$[\begin{matrix} 7 & - 2 & - 4 & 16 \\ - 3 & 1 & 2 & - 7 \\ 6 & - 2 & - 4 & 14 \end{matrix}]$

Step 2

Following sequence of operations is used to reduce the augmented matrix.

$[\begin{matrix} 7 & - 2 & - 4 & 16 \\ - 3 & 1 & 2 & - 7 \\ 6 & - 2 & - 4 & 14 \end{matrix}] R_{1} \to R_{1} - R_{2} [\begin{matrix} 1 & 0 & 0 & 2 \\ - 3 & 1 & 2 & - 7 \\ 6 & - 2 & - 4 & 14 \end{matrix}] R_{3} \to R_{3} + 2 R_{2} [\begin{matrix} 1 & 0 & 0 & 2 \\ - 3 & 1 & 2 & - 7 \\ 0 & 0 & 0 & 0 \end{matrix}] R_{2} \to R_{2} + 3 R_{1} [\begin{matrix} 1 & 0 & 0 & 2 \\ 0 & 1 & 2 & - 1 \\ 0 & 0 & 0 & 0 \end{matrix}]$

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