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b) The following proposed proof contains two mistakes. Explain the mistakes. Result Let A and B be two nxm matrices. Show that if A is row equivalent to B, then A can be written as a product of a sequence of elementary matrices with B and B can also be written as a product of a sequence of elementary matrices with A. Proof Suppose there exist a sequence of s elementary row operations, R,, R,,..., R, that link A to B, that is A- R R2 RB. Let E, be the respective elementary matrix that associate with the elementary row operation R, for every i e{1,2,..., s}. Then we have A = E,E,...E̟B. Then since every E, is also an elementary matrix, we have B = E,E,...E̟A.

b) The following proposed proof contains two mistakes. Explain the mistakes. Result Let A and B be two nxm matrices. Show that if A is row equivalent to B, then A can be written as a product of a sequence of elementary matrices with B and B can also be written as a product of a sequence of elementary matrices with A. Proof Suppose there exist a sequence of s elementary row operations, R,, R,,..., R, that link A to B, that is A- R R2 RB. Let E, be the respective elementary matrix that associate with the elementary row operation R, for every i e{1,2,..., s}. Then we have A = E,E,...E̟B. Then since every E, is also an elementary matrix, we have B = E,E,...E̟A.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.1: Definition Of A Group
Problem 35E: 35. A permutation matrix is a matrix that can be obtained from an identity matrix by interchanging...
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b) The following proposed proof contains two mistakes. Explain the mistakes. Result Let A and B be two nxm matrices. Show that if A is row equivalent to B, then A can be written as a product of a sequence of elementary matrices with B and B can also be written as a product of a sequence of elementary matrices with A. Proof Suppose there exist a sequence of s elementary row operations, R,, R,,..., R, that link A to B, that is A-R R>B. Let E, be the respective elementary matrix that associate with the elementary row operation R, for every i e{1,2,..., s}. Then we have A = E,E,...E̟B. Then since every E,' is also an elementary matrix, we have B = E,E,...E̟A.
Transcribed Image Text:b) The following proposed proof contains two mistakes. Explain the mistakes. Result Let A and B be two nxm matrices. Show that if A is row equivalent to B, then A can be written as a product of a sequence of elementary matrices with B and B can also be written as a product of a sequence of elementary matrices with A. Proof Suppose there exist a sequence of s elementary row operations, R,, R,,..., R, that link A to B, that is A-R R>B. Let E, be the respective elementary matrix that associate with the elementary row operation R, for every i e{1,2,..., s}. Then we have A = E,E,...E̟B. Then since every E,' is also an elementary matrix, we have B = E,E,...E̟A.
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