Linear (in)dependent vector sets

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Discussion Overview

The discussion centers on the linear independence of the vector set consisting of the functions 6, 3*(sinx)^2, and 2*(cosx)^2. Participants seek to understand how to determine linear independence and the implications of this concept.

Discussion Character

  • Exploratory, Conceptual clarification, Homework-related

Main Points Raised

  • One participant asks whether the functions 6, 3*(sinx)^2, and 2*(cosx)^2 are linearly independent and requests an explanation of how to determine this.
  • Another participant suggests using the Pythagorean identity, sin^2(x) + cos^2(x) = 1, as a potential tool for solving the problem.
  • A participant expresses uncertainty about how to apply the Pythagorean identity to the problem at hand.
  • Another participant questions the meaning of linear independence, indicating a need for clarification on the concept itself.

Areas of Agreement / Disagreement

There is no consensus on the linear independence of the functions, and multiple viewpoints regarding the application of the Pythagorean identity and the definition of linear independence are present.

Contextual Notes

Participants have not yet provided a complete method for determining linear independence, and there are unresolved questions regarding the application of mathematical identities in this context.

Who May Find This Useful

Students and individuals interested in linear algebra, particularly those exploring concepts of linear independence and the application of trigonometric identities.

madking153
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are 6, 3*(sinx)^2 and 2*(cosx)^2 - linearly independent ?

Can someone explain how to determine it ?
 
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What have you tried?

You might want to make use of the Pythagorean identity (that sin^2(x) + cos^2(x) = 1).
 
how i use the identity to solve that problem
 
well, what does it mean for things to be linearly independent?
 

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