Explanation Given information: The system of equations is as follows. a 1 x + b 1 y = c 1 a 2 x + b 2 y = c 2 Calculation: Refer to Section 5.4 “Solving Systems of Two Linear Equations in Two Unknowns by Determinant” from the textbook. The solutions of the two linear equations are x = c 1 b 2 − c 2 b 1 a 1 b 2 − a 2 b 1 and y = a 1 c 2 − a 2 c 1 a 1 b 2 − a 2 b 1 . Apply Gaussian elimination in the system of equations as shown below. Show the system of equations as shown below. a 1 x + b 1 y = c 1 a 2 x + b 2 y = c 2 Apply the row operation R 2 → R 2 − a 2 a 1 R 1 as shown below. a 1 x + b 1 y = c 1 ( b 2 − a 2 a 1 b 1 ) y = c 2 − a 2 a 1 c 1 Calculate the value of y as shown below. ( a 1 b 2 − a 2 b 1 a 1 ) y = c 2 a 1 − c 1 a 2 a 1 y = a 1 c 2 − a 2 c 1 a 1 b 2 − a 2 b 1 = | a 1 c 1 a 2 c 2 | | a 1 b 1 a 2 b 2 | Substitute a 1 c 2 − a 2 c 1 a 1 b 2 − a 2 b 1 for y in R 1 as shown below

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 16.5, Problem 29E

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Solve the system of equations using Gaussian elimination and show that the result is the same obtained using Cramer’s rule.

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Chapter 16.5, Problem 28E

Chapter 16.5, Problem 30E

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Chapter 16 Solutions

Basic Technical Mathematics

Ch. 16.1 - For matrices A and B, find A + B. Ch. 16.1 - Prob. 2PE Ch. 16.1 - Prob. 3PE Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - In Exercises 3–10, determine the value of the...Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E

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