Finding the Order of a 2x2 Matrix

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Homework Help Overview

The discussion revolves around finding the order of a 2x2 matrix within the context of linear transformations. Participants are exploring definitions and processes related to the concept of "order" in matrices and linear transformations.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster seeks a general explanation of the process for determining the order of a 2x2 matrix without revealing specific details of their problem. Another participant questions the definition of "order of a matrix," leading to a clarification about the distinction between the order of a matrix and the order of a linear transformation.

Discussion Status

The discussion is currently focused on clarifying definitions and exploring the relationship between matrix order and linear transformations. Some guidance has been provided regarding calculating powers of the matrix to determine its order, but there is no explicit consensus on the definitions being used.

Contextual Notes

Participants are navigating different interpretations of the term "order," particularly distinguishing between the order of a matrix and the order of a linear transformation. The original poster has not provided specific numerical details of their matrix, which may affect the discussion.

ns5032
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I have a specific 2 by 2 matrix, but obviously I don't want the answer to my actual problem, so can someone just explain to me the general process of finding the order of a 2x2 matrix??
 
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What is the definition of "order of a matrix"?
 
You know as well as I do. The problem I am given states:

"Given a linear transformation given by the matrix equation:

(x',y') = (x,y) (a specific 2x2 matrix with some number b included, which I will leave out for now),

show that this transformation has order 3, no matter what b is."
 
No, I don't know what definition you are using for "order of a matrix" which is what you asked. The only definition I know would say that the order of a 2 x 2 matrix is "2 x 2".

There is, however, an "order" of a LINEAR TRANSFORMATION which you now mention. It is the smallest power, n, such that Tn is the identity. If that is the definition you are using just calculate the square and third power of your matrix. If the square is not the identity but the third power is, then the linear transformation has "order" 3.
 

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