Explanation Given information: The given matrix is [ 1 2 2 5 ] . Calculation: Consider the given matrix as A . Write the given matrix. A = [ 1 2 2 5 ] Write the given matrix with identity matrix. A = [ 1 2 2 5 | 1 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. In the given matrix the first element value is 1. The element a 21 in Equation (1) should be 0. Subtract row 2 by 2 times of row 1. A = [ 1 2 2 5 | 1 0 0 1 ] → R 2 − 2 R 1 = [ 1 2 2 − 2 ( 1 ) 5 − 2 ( 2 ) | 1 0 0 − 2 ( 1 ) 1 − 2 ( 0 ) ] = [ 1 2 0 1 | 1 0 − 2 1 ] (2) The bottom row element a 22 in Equation (2) should be 1. In Equation (2) the a 22 element value is 1. The top row element a 12 in Equation (2) should be 0. Subtract row 1 by 2 times of row 2. A = [ 1 2 0 1 | 1 0 − 2 1 ] → R 1 − 2 R 2 = [ 1 − 2 ( 0 ) 2 − 2 ( 1 ) 0 1 | 1 − 2 ( − 2 ) 0 − 2 ( 1 ) − 2 1 ] = [ 1 0 0 1 | 5 − 2 − 2 1 ] The given matrix transformed into the identity matrix

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 16.3, Problem 11E

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Find the inverse of the given matrix using Gauss–Jordan method.

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Chapter 16.3, Problem 10E

Chapter 16.3, Problem 12E

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Chapter 16 Solutions

Basic Technical Mathematics

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