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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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