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 + x 2 + x 3 + x 4 = 1 …… (1) 2 x 1 + x 2 − x 3 + x 4 = 0 …… (2) x 1 + x 2 − x 3 = 0 …… (3) x 1 + x 4 = 0 …… (4) To eliminate x 1 divide the equation (2) by 2: x 1 + x 2 + x 3 + x 4 = 1 …… (1) x 1 + 1 2 x 2 − 1 2 x 3 + 1 2 x 4 = 0 …… (5) x 1 + x 2 − x 3 = 0 …… (3) x 1 + x 4 = 0 …… (4) Subtract the equation (3), (5) and (4) from (1): x 1 + x 2 + x 3 + x 4 = 1 …… (1) 1 2 x 2 + 3 2 x 3 + 1 2 x 4 = 1 …… (5) x 2 + x 3 = 1 …… (6) 2 x 3 + x 4 = 1 …… (7) To eliminate x 2 multiple the equation (6) by 2: x 1 + x 2 + x 3 + x 4 = 1 …… (1) x 2 + 3 x 3 + x 4 = 2 …… (5) x 2 + x 3 = 1 …… (8) 2 x 3 + x 4 = 1 …… (7) Subtract the equation (8) from (5): x 1 + x 2 + x 3 + x 4 = 1 …… (1) x 2 + 3 x 3 + x 4 = 2 …… (5) 2 x 3 + x 4 = 1 …… (8) 2 x 3 + x 4 = 1 …… (9) Assign x 4 as free variable s such that − ∞ < s < ∞ , Substitute s for x 4 in the equation (8):

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 4E

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To solve: The system of equation x3+x4=0, x1+x2+x3+x4=1, 2x1−x2+x3+2x4=0 and 2x1−x2+x3+x4=0 using the Gauss-Jordan elimination algorithm.

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Chapter 9.2, Problem 3E

Chapter 9.2, Problem 5E

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Chapter 9 Solutions

Fundamentals of Differential Equations and Boundary Value Problems

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

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

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To solve: The system of equation x3+x4=0, x1+x2+x3+x4=1, 2x1−x2+x3+2x4=0 and 2x1−x2+x3+x4=0 using the Gauss-Jordan elimination algorithm.

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Chapter 9 Solutions