Given a linear transformation, determine matrix A

Click For Summary

Homework Help Overview

The discussion revolves around determining the matrix representation of a linear transformation, specifically focusing on the context of 2x2 matrices and their properties in relation to linear transformations.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the meaning of M_2 and its relation to the matrix A. There is an exploration of whether the given vectors form a basis and how that relates to the matrix representation of the linear transformation.

Discussion Status

The discussion is ongoing, with participants raising questions about the definitions and properties of the matrices involved. Some guidance has been offered regarding the uniqueness of matrix representation once a basis is specified, but no consensus has been reached.

Contextual Notes

There is mention of the notation M2(R) and M2x2, indicating a focus on the set of 2x2 matrices with real number elements. The implications of the basis for the linear transformations are also under consideration.

WK95
Messages
139
Reaction score
1

Homework Statement


LPE6kM6.png



Homework Equations



The Attempt at a Solution


What is M_2 supposed to be? Is A supposed to be the matrix that produces those above linear transformations?
 
Physics news on Phys.org
pretty much, yes. can you determine what the matrix is?
 
WK95 said:

Homework Statement


LPE6kM6.png



Homework Equations



The Attempt at a Solution


What is M_2 supposed to be? Is A supposed to be the matrix that produces those above linear transformations?
M2(R) is the set of 2 X 2 matrices with elements from the field of real numbers. Other notation I've seen is M2x2.
 
Once a basis has been specified, each linear transformation has a unique matrix representation. Think about the vectors that they gave you ##L## acting on. Do they form a basis? If so, how would they be linked to the form of the matrix?
 

Similar threads

What does a row matrix represent geometrically?
  • · Replies 8 ·
Replies
8
Views
1K
Linear algebra invertible transformation of coordinates
  • · Replies 2 ·
Replies
2
Views
1K
Fundamental matrix linear system equivalent to linear matrix system
  • · Replies 2 ·
Replies
2
Views
1K
Row space of a transformation matrix
  • · Replies 1 ·
Replies
1
Views
2K
What is the defect of a linear transformation
  • · Replies 1 ·
Replies
1
Views
3K
Conflicting definitions of linear independence
  • · Replies 30 ·
2
Replies
30
Views
2K
Understanding Isomorphisms for Linear Transformations
  • · Replies 1 ·
Replies
1
Views
1K
Linear Algebra - Standard Matrix of T
  • · Replies 5 ·
Replies
5
Views
2K
Intro to Linear Algebra - Nullspace of Rank 1 Matrix
  • · Replies 8 ·
Replies
8
Views
2K
Linear operator in 2x2 complex vector space
  • · Replies 18 ·
Replies
18
Views
3K