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 third equation. Step-5: Continue above step until all system become uncoupled system. Calculation: Consider the system of equation: x 1 + x 2 + x 3 = i …… (1) 2 x 1 + 3 x 2 − i x 3 = 0 …… (2) x 1 + 2 x 2 + x 3 = i …… (3) To eliminate x 1 divide the equation (2) by 2: x 1 + x 2 + x 3 = i …… (1) x 1 + 3 2 x 2 − i 2 x 3 = 0 …… (2) x 1 + 2 x 2 + x 3 = i …… (4) Subtract the equation (2) and (4) from (1): x 1 + x 2 + x 3 = i …… (1) − 1 2 x 2 + ( 1 + i 2 ) x 3 = i …… (5) − x 2 = 0 …… (6) Solve above uncoupled equations separately: x 2 = 0 Substitute 0 for x 2 in the equation (5): ( 0 ) x 2 + ( 1 + i 2 ) x 3 = i ( 1 + i 2 ) x 3 = i Solve for x 3 ,

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 9.2, Problem 10E

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The system of equation x1+x2+x3=i, 2x1+3x2−ix3=0 and x1+2x2+x3=i using the Gauss-Jordan elimination algorithm.

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Chapter 9.2, Problem 9E

Chapter 9.2, Problem 11E

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Fundamentals of Differential Equations and Boundary Value Problems

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The system of equation x 1 + x 2 + x 3 = i , 2 x 1 + 3 x 2 − i x 3 = 0 and x 1 + 2 x 2 + x 3 = i 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+x2+x3=i, 2x1+3x2−ix3=0 and x1+2x2+x3=i using the Gauss-Jordan elimination algorithm.

Want to see the full answer?

Chapter 9 Solutions

The system of equation x 1 + x 2 + x 3 = i , 2 x 1 + 3 x 2 − i x 3 = 0 and x 1 + 2 x 2 + x 3 = i 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+x2+x3=i, 2x1+3x2−ix3=0 and x1+2x2+x3=i using the Gauss-Jordan elimination algorithm.

Want to see the full answer?

Chapter 9 Solutions

To solve:

The system of equation x1+x2+x3=i, 2x1+3x2−ix3=0 and x1+2x2+x3=i using the Gauss-Jordan elimination algorithm.