Explanation Given information: The given matrix is [ 1 2 − 1 3 7 − 5 − 1 − 2 0 ] . Calculation: Consider the given matrix as A . Write the given matrix. A = [ 1 2 − 1 3 7 − 5 − 1 − 2 0 ] Write the given matrix with identity matrix. A = [ 1 2 − 1 3 7 − 5 − 1 − 2 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. Replace the elements of row 2 by subtracting 3 times each element of row 1 from the corresponding element in row 2 and Replace the elements of row 3 by adding element of row 1 from the corresponding element in row 3. A = [ 1 2 − 1 3 7 − 5 − 1 − 2 0 | 1 0 0 0 1 0 0 0 1 ] R 2 ⇒ R 2 − 3 R 1 R 3 ⇒ R 3 + R 1 = [ 1 2 − 1 3 − 3 ( 1 ) 7 − 3 ( 2 ) − 5 − 3 ( − 1 ) − 1 + 1 − 2 + 2 0 − 1 | 1 0 0 0 − 3 ( 1 ) 1 − 3 ( 0 ) 0 − 3 ( 0 ) 0 + 1 0 + 0 1 + 0 ] = [ 1 2 − 1 0 1 − 2 0 0 − 1 | 1 0 0 − 3 1 0 1 0 1 ] (2) The bottom row element a 22 in Equation (2) should be 1. The value of element a 22 is 1. The elements a 12 and a 32 in Equation (2) should be zero. The value of a 32 element is already 1. Replace the elements of row 1 by subtracting 2 times each element of row 2 from the corresponding element in row 1. A = [ 1 2 − 1 0 1 − 2 0 0 − 1 | 1 0 0 − 3 1 0 1 0 1 ] R 1 ⇒ R 1 − 2 R 2 = [ 1 − 2 ( 0 ) 2 − 2 ( 0 ) − 1 − 2 ( − 2 ) 0 1 − 1 0 0 − 1 | 1 − 2 ( − 3 ) 0 − 2 ( 1 ) 0 − 2 ( 0 ) − 3 1 0 1 0 1 ] = [ 1 0 3 0 1 − 2 0 0 − 1 | 7 − 2 0 − 3 1 0 1 0 1 ] (3) The bottom row element a 33 in Equation (3) should be 1. Replace the row 3 elements by dividing with –1 with each element. A = [ 1 0 3 0 1 − 2 0 0 − 1 | 7 − 2 0 − 3 1 0 1 0 1 ] R 3 ⇒ R 3 − 1 = [ 1 0 3 0 1 − 2 0 − 1 0 − 1 − 1 − 1 | 7 − 2 0 − 3 1 0 1 − 1 0 − 1 1 − 1 ] = [ 1 0 3 0 1 − 2 0 0 1 | 7 − 2 0 − 3 1 0 − 1 0 − 1 ] (4) The top row element a 13 and second row element a 23 in Equation (4) should be 0

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 16.3, Problem 18E

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Chapter 16.3, Problem 17E

Chapter 16.3, Problem 19E

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Chapter 16 Solutions

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