MHB Choose from the following set of vectors in R4

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The discussion revolves around identifying the maximum number of linearly independent vectors from a given set in R4. The user initially calculates the rank of the matrix formed by the vectors as 4 but struggles to apply this to the question. They conclude that vectors 2, 3, 4, and 5 are independent after omitting vector 1, which is a multiple of vector 2. Another participant suggests that vectors 1, 3, 4, and 5 could also be a valid independent set, indicating multiple correct answers. Ultimately, the user confirms their answer was correct, despite their uncertainty about the reasoning.
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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