Can Any Matrix be Reduced to a Canonical Matrix?

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Homework Help Overview

The discussion revolves around the concept of reducing matrices to a canonical form, specifically focusing on whether any matrix can be transformed into such a form. The subject area pertains to linear algebra and matrix theory.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to assert that any matrix can be reduced to a canonical form, questioning the conditions under which a linear system may have no solutions. Other participants inquire about the specific definition of a 'canonical' matrix and suggest different forms such as Jordan canonical form and reduced row echelon form.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of what constitutes a canonical matrix. Some guidance is offered regarding the types of canonical forms, but no consensus has been reached on the original poster's assertion.

Contextual Notes

daniel_i_l
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Homework Statement


I have a question that doesn't relate to a specific problem:
Can any matrix be reduced to a canonical matrix?

Homework Equations



the three elementry operations

The Attempt at a Solution



I think that the answer is yes and that the only way that a linear system has no answer is when the lowest non-zero row has the form of: (0,..,0,1)
Is that right?
Thanks.
 
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What is a 'canonical' matrix? Jordan canonical form? Row echelon form? Reduced row echelon form?
 
Reduced row echelon form.
 
Have you tried to put matrices in row ecehlon for using the operations? It's always worked, right. NOw, do you need to justify that, or is it just a yes/no question?
 
This wasn't a homework question, i just was asking to see if i understood correctly, so it's a yes/no question.
 

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