Explanation Given information: The given matrix A is [ 1 − 1 1 0 − 2 1 − 2 − 3 0 ] . The given matrix C is [ 5 − 1 0 2 − 2 1 − 3 0 4 ] . Calculation: Use Gauss Jordan method to find the A − 1 value. Write the given matrix with identity matrix. A = [ 1 − 1 1 0 − 2 1 − 2 − 3 0 | 1 0 0 0 1 0 0 0 1 ] (1) The vertical line in Equation (1) denotes the separation of two matrices. The first element in the given matrix should be 1. The value of element a 11 is 1. The elements a 21 and a 31 in Equation (1) should be 0. The element a 21 value is already 0. Replace the elements of row 3 by adding 2 times element of row 1 from the corresponding element in row 3. A = [ 1 − 1 1 0 − 2 1 − 2 − 3 0 | 1 0 0 0 1 0 0 0 1 ] R 3 ⇒ R 3 + 2 R 1 = [ 1 − 1 1 0 − 2 1 − 2 + 2 ( 1 ) − 3 + 2 ( − 1 ) 0 + 2 ( 1 ) | 1 0 0 0 1 0 0 + 2 ( 1 ) 0 + 2 ( 0 ) 1 + 2 ( 0 ) ] = [ 1 − 1 1 0 − 2 1 0 − 5 2 | 1 0 0 0 1 0 2 0 1 ] (2) The bottom row element a 22 in Equation (2) should be 1. Replace the row 2 by dividing –2 with each element in row 2. A = [ 1 − 1 1 0 − 2 1 0 − 5 2 | 1 0 0 0 1 0 2 0 1 ] R 2 ⇒ R 2 − 2 = [ 1 − 1 1 0 − 2 − 2 − 2 1 − 2 0 − 5 2 | 1 0 0 0 − 2 1 − 2 0 − 2 2 0 1 ] = [ 1 − 1 1 0 1 − 1 2 0 − 5 2 | 1 0 0 0 − 1 2 0 2 0 1 ] (3) The elements a 12 and a 32 in Equation (3) should be zero. Replace the elements of row 1 by adding each element of row 2 from the corresponding element in row 1. Replace the elements of row 3 by adding 5 times each element of row 2 from the corresponding element in row 3. A = [ 1 − 1 1 0 1 − 1 2 0 − 5 2 | 1 0 0 0 − 1 2 0 2 0 1 ] R 1 ⇒ R 1 + R 2 R 3 ⇒ R 3 + 5 R 2 = [ 1 + 0 − 1 + 1 1 − 1 2 0 1 − 1 2 0 + 5 ( 0 ) − 5 + 5 ( 1 ) 2 + 5 ( − 1 2 ) | 1 + 0 0 − 1 2 0 + 0 0 − 1 2 0 2 + 5 ( 0 ) 0 + 5 ( − 1 2 ) 1 + 5 ( 0 ) ] = [ 1 0 1 2 0 1 − 1 2 0 0 − 1 2 | 1 − 1 2 0 0 − 1 2 0 2 − 5 2 1 ] (4) The bottom row element a 33 in Equation (4) should be 1. Replace the row 3 elements by dividing − 1 2 with each element. A = [ 1 0 1 2 0 1 − 1 2 0 0 − 1 2 | 1 − 1 2 0 0 − 1 2 0 2 − 5 2 1 ] R 3 ⇒ R 3 − 1 2 = [ 1 0 1 2 0 1 − 1 2 0 − 1 2 0 − 1 2 − 1 2 − 1 2 | 1 − 1 2 0 0 − 1 2 0 2 − 1 2 − 5 2 − 1 2 1 − 1 2 ] A = [ 1 0 1 2 0 1 − 1 2 0 0 1 | 1 − 1 2 0 0 − 1 2 0 − 4 5 − 2 ] (5) The top row element a 13 and second row element a 23 in Equation (5) should be 0

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 16.3, Problem 33E

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Find the matrix value of CA−1.

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Chapter 16.3, Problem 32E

Chapter 16.3, Problem 34E

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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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Prob. 77RE Ch. 16 - Prob. 78RE Ch. 16 - Prob. 79RE Ch. 16 - Prob. 80RE Ch. 16 - Prob. 81RE Ch. 16 - Prob. 82RE Ch. 16 - Prob. 83RE Ch. 16 - Prob. 84RE Ch. 16 - Prob. 85RE Ch. 16 - Prob. 86RE Ch. 16 - Prob. 87RE Ch. 16 - Prob. 88RE Ch. 16 - Prob. 89RE Ch. 16 - Prob. 90RE Ch. 16 - Prob. 91RE Ch. 16 - Prob. 92RE Ch. 16 - Prob. 93RE Ch. 16 - Prob. 94RE Ch. 16 - Prob. 95RE Ch. 16 - Prob. 96RE Ch. 16 - Prob. 97RE Ch. 16 - Prob. 1PT Ch. 16 - Prob. 2PT Ch. 16 - Prob. 3PT Ch. 16 - Prob. 4PT Ch. 16 - Prob. 5PT Ch. 16 - Prob. 6PT Ch. 16 - Prob. 7PT Ch. 16 - Prob. 8PT Ch. 16 - Prob. 9PT Ch. 16 - Prob. 10PT

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Chapter 16 Solutions