Choose from the following set of vectors in R4

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Discussion Overview

The discussion revolves around identifying the maximum number of linearly independent vectors from a given set in R4. Participants explore the implications of linear dependence among the vectors and how it affects the selection of independent vectors.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant notes that the second vector is a multiple of the first, suggesting that it can be excluded from consideration.
  • Another participant agrees with the exclusion of the first two vectors and proposes that the remaining vectors (2, 3, 4, 5) are independent.
  • A different participant suggests that including vectors 1, 3, 4, and 5 could also yield a valid set of independent vectors.
  • One participant expresses uncertainty about the reasoning behind their answer being correct on a test, despite not fully understanding the underlying concepts.

Areas of Agreement / Disagreement

Participants do not reach a consensus on which specific vectors constitute the maximum set of linearly independent vectors, as multiple competing views are presented.

Contextual Notes

There is uncertainty regarding the reasoning behind the selection of vectors, and participants express differing opinions on which vectors can be omitted based on linear dependence.

Who May Find This Useful

This discussion may be useful for individuals studying linear algebra, particularly those interested in vector independence and matrix rank in R4.

forzi
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Hi everybody,

I have a problem with this question:
Choose from the following set of vectors in R4 set of the maximum number of linearly independent vectors:
1.(1;2;3;4) 2.(2;4;6;8) 3.(0;1;-1;1) 4.(1;1;1;0) 5.(0;3;0;0)

So, I can find a rank of a matrix, it's 4, but I can't understand how it could help me answering my question.

Would you please help me?
 
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I can just assume that cause second vector is equal 2*first vector, I can remove first vector from calculation and the answer will be 2,3,4,5
tBut it just an assumption.
 
Hi forzi and welcome to MHB! :D

I think you have the right idea but wouldn't one omit vectors 1. and 2.?
 
Hi greg

Thanks :)
I can't understand your question. But I can say that answer to my question is 2,3,4,5. I finished the test with this answer and it was right.
Have no idea why :confused:
 
Wouldn't vectors 1,3,4,5 be an equally good answer?
 

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