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

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Homework Help Overview

The discussion revolves around finding change of basis matrices for the polynomial space R2[x] using two different bases, B and B'. The original poster expresses difficulty in approaching the problem due to a lack of foundational knowledge on the topic.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants inquire about the original poster's prior knowledge and attempts, suggesting a need to understand linear transformations and how to express vectors in one basis as combinations of another.

Discussion Status

The discussion is ongoing, with some participants providing guidance on foundational concepts and suggesting resources for further reading. There is no explicit consensus on how to proceed, as the original poster has not yet engaged with the material.

Contextual Notes

The original poster indicates they have missed relevant coursework, which may limit their understanding of the problem. There is a suggestion that they should seek additional help from a teacher or review their textbook before attempting the problem.

masp3
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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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