Given a linear transformation, determine matrix A

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SUMMARY

The discussion centers on determining the matrix A that represents a given linear transformation in the context of M2(R), the set of 2x2 matrices with real number elements. Participants clarify that A is indeed the matrix that produces the specified linear transformations. It is emphasized that once a basis is established, each linear transformation can be uniquely represented by a matrix. The relationship between the vectors provided and the matrix form is crucial for understanding the transformation.

PREREQUISITES
  • Understanding of linear transformations
  • Familiarity with matrix representation in M2(R)
  • Knowledge of basis vectors in vector spaces
  • Concept of unique matrix representation for linear transformations
NEXT STEPS
  • Study the properties of linear transformations and their matrix representations
  • Learn about basis vectors and their role in defining transformations
  • Explore examples of linear transformations in M2(R)
  • Investigate the relationship between linear transformations and eigenvalues
USEFUL FOR

Students and educators in linear algebra, mathematicians working with matrix theory, and anyone seeking to understand the application of linear transformations in 2x2 matrices.

WK95
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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?
 
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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?
 

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