A simple Linear Algebra question that seems so hard

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Homework Help Overview

The discussion revolves around the properties of determinants in linear algebra, specifically whether the determinant of a matrix remains unchanged when the columns are reversed. Participants are exploring the implications of this property and seeking justification for their reasoning.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand the relationship between column order and the determinant, noting a change in sign. Others inquire about methods for calculating determinants, such as cofactor expansion, and how this method would be affected by switching columns.

Discussion Status

The discussion is ongoing, with participants sharing insights about determinant calculation methods and questioning how these methods relate to the property in question. There is a focus on understanding the underlying principles rather than reaching a definitive conclusion.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the depth of exploration into proofs or detailed explanations.

qwerty11
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Homework Statement



Is the statement true or sometimes false. Justify your answer:

The determinant of a matrix is unchanged if the columns are written in reverse order.

Homework Equations





The Attempt at a Solution



I understand that the only thing that is changed is the sign (negative to positive or visa-versa), but do not understand the proof of how.
 
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how do you find the determinant of a matrix?
 
One way would be via cofactor expansion.

I.e. 3x3 matrix determinant =a11C11+a12C12+a13C13
 
okay good. so if you switched the columns, how would the cofactor expansion change?
 
and calculate out those cofactors when you do it.
 

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