Example of a linear transformation T: p4 -> R^4 thats onto

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Homework Help Overview

The discussion revolves around finding an example of a linear transformation from the space of polynomials of degree at most four, denoted as p4, to R^4, with a specific focus on demonstrating that this transformation is onto. Participants are tasked with understanding the properties of linear transformations and the concept of being onto.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to start with the definition of "onto" and suggest that a simple example of a linear transformation should be established first. There is also a mention of needing to prove the transformation is one-to-one as part of the process.

Discussion Status

The discussion is ongoing, with participants expressing confusion and seeking clarification on how to approach the problem. Some guidance has been offered regarding the definitions and the need for an example, but no consensus or clear direction has been reached yet.

Contextual Notes

Participants are working under the constraints of needing to provide a specific example of a linear transformation and prove its properties, which may involve definitions and theorems related to linear algebra.

sportlover36
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in my book it asks me to give an example of a linear transformation T: p4 -> R^4 that's onto. I have to prove that T is onto and a linear transformation...can someone give me some advice?
 
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Start with the definition of "onto."
 
Actually, start with giving a simple example of a linear transformation- you have to have the transformation before you can prove it is one-to-one!

Then use the definition of "onto".
 
im still confused
 
Can you think of any transformation that takes a polynomial such as x^4 + 5x^3 - x^2 + 2x - 5 to a vector with four components?
 

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