Explanation Formula used: The procedure to solve the system of liner equation using Gauss –elimination, Step-1: The first unknown x 1 is eliminated from the last remaining equations by subtracting multiples of the first equation. Step-2: The second unknown x 2 is eliminated from the last remaining equations by subtracting multiples of the reduced second equation. Step-3: The third unknown x 3 is eliminated from the last remaining equations by subtracting multiples of the reduced third equation. Step-4: The nth unknown x n is eliminated from the last remaining equations by subtracting multiples of the reduced nth equation. Step-5: Continue above step until all system becomes uncoupled system. Calculation: Consider the system of equation: x 1 + 2 x 2 + x 3 = − 3 …… (1) 2 x 1 + 4 x 2 − x 3 = 0 …… (2) x 1 + 3 x 2 − 2 x 3 = 3 …… (3) To eliminate x 1 divide the equation (2) by 2: x 1 + 2 x 2 + x 3 = − 3 …… (1) x 1 + 2 x 2 − 1 2 x 3 = 0 …… (4) x 1 + 3 x 2 − 2 x 3 = 3 …… (3) Subtract the equation (4) and (3) from (1): x 1 + 2 x 2 + x 3 = − 3 …… (1) − x 2 + 3 x 3 = − 6 …… (4) 3 2 x 3 = − 3 …… (3) Solve above uncoupled equations separately: x 3 = − 2 Substitute − 2 for x 3 in the equation (4):

Fundamentals of Differential Equations [With CDROM] - 7th Edition

7th Edition

ISBN: 9780321410481

Author: Saff, Edward B., Snider, Arthur David, Nagle, R. Kent

Publisher: Addison Wesley

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Chapter 9.2, Problem 8E

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To solve: The system of equation

x1+2x2+x3=−3, 2x1+4x2−x3=0 and x1+3x2−2x3=3 using the Gauss-Jordan elimination algorithm.

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Chapter 9.2, Problem 7E

Chapter 9.2, Problem 9E

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Chapter 9 Solutions

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The system of equation x 1 + 2 x 2 + x 3 = − 3 , 2 x 1 + 4 x 2 − x 3 = 0 and x 1 + 3 x 2 − 2 x 3 = 3 using the Gauss-Jordan elimination algorithm.

Solution Summary: The author explains the procedure to solve the system of liner equation using Gauss-Jordan elimination.

Videos

To solve: The system of equation

x1+2x2+x3=−3, 2x1+4x2−x3=0 and x1+3x2−2x3=3 using the Gauss-Jordan elimination algorithm.

Want to see the full answer?

Chapter 9 Solutions

The system of equation x 1 + 2 x 2 + x 3 = − 3 , 2 x 1 + 4 x 2 − x 3 = 0 and x 1 + 3 x 2 − 2 x 3 = 3 using the Gauss-Jordan elimination algorithm.

Solution Summary: The author explains the procedure to solve the system of liner equation using Gauss-Jordan elimination.

Videos

To solve: The system of equation x1+2x2+x3=−3, 2x1+4x2−x3=0 and x1+3x2−2x3=3 using the Gauss-Jordan elimination algorithm.

Want to see the full answer?

Chapter 9 Solutions

To solve: The system of equation

x1+2x2+x3=−3, 2x1+4x2−x3=0 and x1+3x2−2x3=3 using the Gauss-Jordan elimination algorithm.