Change of Basis Matrices for R2[x] with B and B

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SUMMARY

The discussion focuses on finding the change of basis matrices for the polynomial vector spaces R2[x] with the bases B={1,x,x^2} and B'={1,1-x,x^2-4x+2}. Participants emphasize the necessity of expressing the vectors in basis B as linear combinations of the vectors in basis B'. A clear understanding of linear transformations and the concept of "change of basis" is essential for solving this problem. Resources such as online tutorials are recommended for further clarification.

PREREQUISITES
  • Understanding of linear transformations and their representation as matrices
  • Familiarity with polynomial vector spaces, specifically R2[x]
  • Knowledge of basis vectors and linear combinations
  • Concept of change of basis in linear algebra
NEXT STEPS
  • Study the process of expressing vectors in one basis as linear combinations of another basis
  • Learn how to compute change of basis matrices in linear algebra
  • Review the concept of linear transformations and their matrix representations
  • Explore online resources on change of basis, such as the tutorial from Harvey Mudd College
USEFUL FOR

Students studying linear algebra, particularly those focusing on polynomial vector spaces and change of basis concepts. This discussion is beneficial for anyone needing assistance with linear transformations and matrix representations.

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consider the basis B={1,x,x^2} and B'={1,1-x,x^2-4x+2} for R2[x]. Find the change of basis matricses [id]B'toB and [id]BtoB'

Really stuck on this! anyone can help me please?
 
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What have you done to start with? What do you know about writing linear transformations as matrices to begin with?

One of the things you will need to do is write the vectors in basis B as linear combinations of the vectors in base B'. Can you do that?
 
I have done nothing to start with and don't know what to do as I missed this part of the course!
 
Then you should not be doing this problem until you have talked to your teacher or at least reviewed this in your textbook.
 
Firstly do you know what does "change of basis" mean in the first place? I found something online which you may want to read through:
http://www.math.hmc.edu/calculus/tutorials/changebasis/
 

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