Understanding the Matrix of Minors

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Discussion Overview

The discussion centers around the concept of the matrix of minors in the context of linear algebra, specifically in relation to a given matrix equation. Participants explore the definition and calculation of the matrix of minors, as well as its distinction from the adjoint matrix.

Discussion Character

  • Technical explanation, Conceptual clarification, Homework-related

Main Points Raised

  • One participant seeks clarification on the matrix of minors, indicating a lack of understanding of the term.
  • Another participant suggests that the term "minors of a matrix" might be what is being referred to.
  • A participant provides a specific matrix equation and asks if the matrix of minors is synonymous with the adjoint matrix.
  • Another participant explains that the matrix of minors consists of the minors of each element in the matrix, clarifying that this is not the same as the adjoint matrix, which involves cofactors and transposition.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the terminology and definitions, as there is some confusion regarding the relationship between the matrix of minors and the adjoint matrix.

Contextual Notes

There is a potential misunderstanding regarding the definitions of the matrix of minors and the adjoint matrix, which may depend on the specific context or definitions being used.

bill nye scienceguy!
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can anyone explain to me what the matrix of minors is?
 
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Is it possible you mean the minors of a matrix?
 
no, I've been given the question:

Ax=b.A=(301), x= transverse of {x,y,z} and b=transverse of {5,2,-1}
(132)
(120)

and the first thing it asks me to do is calculate the matrix of minors. is this just another term for the adjoint matrix or something?
 
Well the "matrix of minors" (of a square matrix) would be the matrix where each element is the minor of the number which was in that position, which isn't the same as the adjoint yet.
For the adjoint, you'd have to take the cofactors (which is the minors + sign taken into account) and transpose that. So adjoint = transpose of cofactor matrix.
 

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