Choose from the following set of vectors in R4

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SUMMARY

The discussion focuses on identifying the maximum number of linearly independent vectors from a given set in R4. The vectors presented are (1;2;3;4), (2;4;6;8), (0;1;-1;1), (1;1;1;0), and (0;3;0;0). Participants concluded that vectors 2, 3, 4, and 5 can be selected as linearly independent, while vector 1 can be omitted due to its linear dependence on vector 2. The correct answer confirmed by the test was indeed vectors 2, 3, 4, and 5.

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  • Understanding of linear independence in vector spaces
  • Familiarity with R4 and vector notation
  • Knowledge of matrix rank and its implications
  • Basic skills in linear algebra concepts
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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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