Explanation Given information: The given Equations are, 4 x + y = 2 , − 2 x − y + 3 z = − 18 , and 2 x + y − z = 8 . Calculation: Use the given information and form matrix A. A = [ 4 1 0 − 2 − 1 3 2 1 − 1 ] Express the unit matrix I as follows: I = [ 1 0 0 0 1 0 0 0 1 ] Determine the value of A − 1 using the relation. A − 1 = A I Substitute [ 4 1 0 − 2 − 1 3 2 1 − 1 ] for A and [ 1 0 0 0 1 0 0 0 1 ] for I . A − 1 = [ 4 1 0 − 2 − 1 3 2 1 − 1 | 1 0 0 0 1 0 0 0 1 ] → R 1 → 1 4 R 1 , R 2 → R 2 + 1 2 R 1 , and R 3 → R 3 − 1 2 R 1 = [ 4 ( 1 4 ) 1 ( 1 4 ) 0 ( 1 4 ) − 2 + ( 1 2 × 4 ) − 1 + ( 1 2 × 1 ) 3 + ( 1 2 × 0 ) 2 − ( 1 2 × 4 ) 1 − ( 1 2 × 1 ) − 1 − ( 1 2 × 0 ) | 1 ( 1 4 ) 0 ( 1 4 ) 0 ( 1 4 ) 0 + ( 1 2 × 1 ) 1 + ( 1 2 × 0 ) 0 + ( 1 2 × 0 ) 0 − ( 1 2 × 1 ) 0 ( 1 2 ) 1 − ( 1 2 × 0 ) ] = [ 1 1 4 0 0 − 1 2 3 0 1 2 − 1 | 1 4 0 0 1 2 1 0 − 1 2 0 1 ] → R 1 → R 1 + 1 2 R 2 , R 2 → − 2 R 2 , and R 3 → R 2 + R 3 A − 1 = [ 1 + ( 1 2 × 0 ) 1 4 + ( 1 2 × − 1 2 ) 3 2 − 2 ( 0 ) − 2 ( − 1 2 ) − 2 ( 3 ) 0 + 0 1 2 + ( − 1 2 ) − 1 + 3 | 1 4 + ( 1 2 × 1 2 ) 0 + ( 1 2 × 1 ) 0 + ( 1 2 × 0 ) − 2 ( 1 2 ) − 2 ( 1 ) − 2 ( 0 ) − 1 2 + 1 2 0 + 1 1 + 0 ] = [ 1 0 3 2 0 1 − 6 0 0 2 | 1 2 1 2 0 − 1 − 2 0 0 1 1 ] → R 1 → R 1 − 3 4 R 3 , R 2 → R 2 + 3 R 3 , and R 3 → 1 2 R 3 = [ 1 − ( 3 4 × 0 ) 0 − ( 3 4 × 0 )

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 16.4, Problem 16E

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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

Ch. 16.1 - Prob. 8E Ch. 16.1 - In Exercises 3–10, determine the value of the...Ch. 16.1 - Prob. 10E Ch. 16.1 - Prob. 11E Ch. 16.1 - Prob. 12E Ch. 16.1 - Prob. 13E Ch. 16.1 - Prob. 14E Ch. 16.1 - Prob. 15E Ch. 16.1 - Prob. 16E Ch. 16.1 - Prob. 17E Ch. 16.1 - Prob. 18E Ch. 16.1 - Prob. 19E Ch. 16.1 - Prob. 20E Ch. 16.1 - Prob. 21E Ch. 16.1 - Prob. 22E Ch. 16.1 - Prob. 23E Ch. 16.1 - Prob. 24E Ch. 16.1 - Prob. 25E Ch. 16.1 - Prob. 26E Ch. 16.1 - Prob. 27E Ch. 16.1 - Prob. 28E Ch. 16.1 - Prob. 29E Ch. 16.1 - Prob. 30E Ch. 16.1 - Prob. 31E Ch. 16.1 - Prob. 32E Ch. 16.1 - Prob. 33E Ch. 16.1 - Prob. 34E Ch. 16.1 - Prob. 35E Ch. 16.1 - Prob. 36E Ch. 16.1 - Prob. 37E Ch. 16.1 - Prob. 38E Ch. 16.1 - Prob. 39E Ch. 16.1 - Prob. 40E Ch. 16.1 - Prob. 41E Ch. 16.1 - Prob. 42E Ch. 16.1 - Prob. 43E Ch. 16.1 - Prob. 44E Ch. 16.2 - Prob. 1PE Ch. 16.2 - Prob. 2PE Ch. 16.2 - Prob. 3PE Ch. 16.2 - Prob. 1E Ch. 16.2 - Prob. 2E Ch. 16.2 - Prob. 3E Ch. 16.2 - Prob. 4E Ch. 16.2 - Prob. 5E Ch. 16.2 - Prob. 6E Ch. 16.2 - 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Chapter 16 Solutions