Explanation Given information: 5 x 1 − 2 x 2 + 6 x 3 = 0 − 2 x 1 + 4 x 2 + x 3 + 3 x 4 = 18 6 x 1 + x 2 + 6 x 3 + 8 x 4 = − 29 3 x 2 + 8 x 3 + 7 x 4 = 11 Calculation: Write the system in the matrix form: Ax = P [ 5 − 2 6 0 − 2 4 1 3 6 1 6 8 0 3 8 7 ] [ x 1 x 2 x 3 x 4 ] = [ 0 18 − 29 11 ] Write the augmented matrix: [ 5 − 2 6 0 − 2 4 1 3 6 1 6 8 0 3 8 7 | 0 18 − 29 11 ] Divide the first row by 5. [ 1 − 2 5 6 5 0 − 2 4 1 3 6 1 6 8 0 3 8 7 | 0 18 − 29 11 ] In the second row, subtract the first row multiplied with 2 from second row. [ 1 − 2 5 6 5 0 − 2 4 1 3 6 1 6 8 0 3 8 7 | 0 18 − 29 11 ] R 2 → R 2 − ( − 2 ) R 1 [ 1 − 2 5 6 5 0 − 2 − ( − 2 × 1 ) 4 − ( − 2 × − 2 5 ) 1 − ( − 2 × 6 5 ) 3 6 1 6 8 0 3 8 7 | 0 18 − 29 11 ] [ 1 − 2 5 6 5 0 0 16 5 17 5 3 6 1 6 8 0 3 8 7 | 0 18 − 29 11 ] In the third row, subtract the first row multiplied with 6 from third row. [ 1 − 2 5 6 5 0 0 16 5 17 5 3 6 1 6 8 0 3 8 7 | 0 18 − 29 11 ] R 3 → R 3 − 6 R 1 [ 1 − 2 5 6 5 0 0 16 5 17 5 3 6 − 6 × 1 1 − 6 × ( − 2 5 ) 6 − 6 × ( 6 5 ) 8 − 6 × ( 0 ) 0 3 8 7 | 0 18 − 29 11 ] [ 1 − 2 5 6 5 0 0 16 5 17 5 3 0 17 5 − 6 5 8 0 3 8 7 | 0 18 − 29 11 ] Divide the second row by 16/5. [ 1 − 2 5 6 5 0 0 1 17 16 15 16 0 17 5 − 6 5 8 0 3 8 7 | 0 45 8 − 29 11 ] In the first row, subtract the second row multiplied with − 2 5 from first row. [ 1 − 2 5 6 5 0 0 1 17 16 15 16 0 17 5 − 6 5 8 0 3 8 7 | 0 45 8 − 29 11 ] R 1 → R 1 − ( − 2 5 R 2 ) [ 1 − 2 5 − ( − 2 5 × 1 ) 6 5 − ( − 2 5 × 17 16 ) 0 − ( − 2 5 × 15 16 ) 0 1 17 16 15 16 0 17 5 − 6 5 8 0 3 8 7 | 0 − ( − 2 5 × 45 8 ) 45 8 − 29 11 ] [ 1 0 13 8 3 8 0 1 17 16 15 16 0 17 5 − 6 5 8 0 3 8 7 | 9 4 45 8 − 29 11 ] In the third row, subtract the second row multiplied with 17 5 from third row. [ 1 0 13 8 3 8 0 1 17 16 15 16 0 17 5 − 6 5 8 0 3 8 7 | 9 4 45 8 − 29 11 ] R 3 → R 3 − ( 17 5 ) R 2 [ 1 0 13 8 3 8 0 1 17 16 15 16 0 17 5 − ( 17 5 × 1 ) − 6 5 − ( 17 5 × 17 16 ) 8 − ( 17 5 × 15 16 ) 0 3 8 7 | 9 4 45 8 − 29 − ( 17 5 × 45 8 ) 11 ] [ 1 0 13 8 3 8 0 1 17 16 15 16 0 0 − 77 16 77 16 0 3 8 7 | 9 4 45 8 − 385 8 11 ] In the fourth row, subtract the second row multiplied with 3 from fourth row. [ 1 0 13 8 3 8 0 1 17 16 15 16 0 0 − 77 16 77 16 0 3 8 7 | 9 4 45 8 − 385 8 11 ] R 4 → R 4 − 3 R 2 [ 1 0 13 8 3 8 0 1 17 16 15 16 0 0 − 77 16 77 16 0 3 − 3 × 1 8 − 3 × 17 16 7 − 3 × 15 16 | 9 4 45 8 − 385 8 11 − 3 × 45 8 ] [ 1 0 13 8 3 8 0 1 17 16 15 16 0 0 − 77 16 77 16 0 0 77 16 67 16 | 9 4 45 8 − 385 8 − 47 8 ] Divide the third row by − 77 16

5th Edition

ISBN: 9780100469105

Author: KASSIMALI

Publisher: YUZU

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Dimensional homogeneity

The term dimensional homogeneity means that in an equation, the dimensions of each term on both sides are equal, which means the dimensions of the left-hand side (LHS) of an equation are similar to the dimensions of the right-hand side (RHS). For a dimen…

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Chapter B, Problem 8P

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Use the Gauss Jordan method to solve the simultaneous equations.

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Chapter B, Problem 7P

Chapter B, Problem 9P

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Chapter B Solutions

EBK STRUCTURAL ANALYSIS

Ch. B - Prob. 1P Ch. B - Prob. 2P Ch. B - Prob. 3P Ch. B - Prob. 4P Ch. B - Prob. 5P Ch. B - Prob. 6P Ch. B - Prob. 7P Ch. B - Prob. 8P Ch. B - Prob. 9P Ch. B - Prob. 10P

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Use the Gauss Jordan method to solve the simultaneous equations.

Solution Summary: The author explains how to solve simultaneous equations using the Gauss Jordan method.

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Use the Gauss Jordan method to solve the simultaneous equations.

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Chapter B Solutions