Lect9a

# Lect9a - Chapter 1. Matrices and Systems of Equations...

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Unformatted text preview: Chapter 1. Matrices and Systems of Equations Math1111 Elementary Matrices Finding inverses (Cont’d) Ans . Refer to p.66 of textbook:      1 4 3- 1- 2 2 2 3 1 1 1     -------------→       1 1 1- 1 2- 1 2 1 2 1 4- 1 4- 1 4 1 6 1 2 1 6       via the following eight elementary row operations: R 1 + R 2- 2 R 1 + R 3 3 R 2 + R 3- 1 2 R 3 + R 1- 1 2 R 3 + R 2- 2 R 2 + R 1 1 2 R 2 1 6 R 3 Chapter 1. Matrices and Systems of Equations Math1111 Elementary Matrices Finding inverses (Cont’d) Ans . Refer to p.66 of textbook:      1 4 3- 1- 2 2 2 3 1 1 1     -------------→       1 1 1- 1 2- 1 2 1 2 1 4- 1 4- 1 4 1 6 1 2 1 6       via the following eight elementary row operations: R 1 + R 2- 2 R 1 + R 3 3 R 2 + R 3- 1 2 R 3 + R 1 E 1 E 2 E 3 E 4- 1 2 R 3 + R 2- 2 R 2 + R 1 1 2 R 2 1 6 R 3 E 5 E 6 E 7 E 8 E i is the corresponding elementary matrix. Chapter 1. Matrices and Systems of Equations Math1111 Elementary Matrices Finding inverses (Cont’d) Ans . Refer to p.66 of textbook:      1 4 3- 1- 2 2 2 3 1 1 1     -------------→       1 1 1- 1 2- 1 2 1 2 1 4- 1 4- 1 4 1 6 1 2 1 6       via the following eight elementary row operations: R 1 + R 2- 2 R 1 + R 3 3 R 2 + R 3- 1 2 R 3 + R 1 E 1 E 2 E 3 E 4- 1 2 R 3 + R 2- 2 R 2 + R 1 1 2 R 2 1 6 R 3 E 5 E 6 E 7 E 8 E i is the corresponding elementary matrix. i.e. E 8 E 7 ··· E 1 ( A I ) = ( I B ) , ∴ A- 1 = E 8 E 7 ··· E 1 . Chapter 1. Matrices and Systems of Equations Math1111 Elementary Matrices Finding inverses (Cont’d) Ans . Refer to p.66 of textbook:      1 4 3- 1- 2 2 2 3 1 1 1     -------------→       1...
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## This note was uploaded on 04/30/2010 for the course MATH 1111 taught by Professor Dr,li during the Spring '10 term at HKU.

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Lect9a - Chapter 1. Matrices and Systems of Equations...

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