Is A Nonsingular? True or False: Elementary Matrix Factorization Explained

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Homework Help Overview

The discussion revolves around the statement regarding nonsingular matrices and their ability to be factored into a product of elementary matrices. Participants are exploring the validity of this statement and the reasoning behind differing conclusions presented in class versus a textbook.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the reasoning used in class to conclude that the statement is false, with some suggesting a potential misinterpretation of the statement regarding the number of elementary matrices involved in the factorization.

Discussion Status

The discussion is ongoing, with participants actively seeking clarification on the reasoning behind the differing conclusions. Some guidance has been offered regarding the interpretation of the statement, but no consensus has been reached.

Contextual Notes

There is mention of a discrepancy between the class conclusion and the textbook's assertion, indicating a need for further examination of the definitions and assumptions related to nonsingular matrices and elementary matrices.

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Homework Statement


If A is nonsingular, then A can be factored into a product of elementary matrices.
True or False but justify the reason.


Homework Equations


The issue here is that in class we came to the conclusion false but the book says true. Can someone help me with the correct answer and reasoning? Thanks.
 
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What was the reasoning your class used to conclude the statement was false?
 


Because the multiplication of two elementary matrices equals the prodct of two elementary martices and the product may not be one step away from I.
 


I don't follow how that leads to the conclusion that a non-singular matrix can't be written as a product of elementary matrices.

I think perhaps you're misinterpreting the statement. It's not saying that A=T1T2, where it's the product of only two elementary matrices. It will generally be the product of more than two elementary matrices.
 

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