Choose from the following set of vectors in R4

In summary, the question is asking to choose the maximum number of linearly independent vectors from a given set in R4. The rank of the matrix can be used to find the answer, but the exact method is not clear. The conversation ends with a suggestion that vectors 1,3,4,5 could also be a valid answer.
  • #1
forzi
3
0
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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  • #2
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.
 
  • #3
Hi forzi and welcome to MHB! :D

I think you have the right idea but wouldn't one omit vectors 1. and 2.?
 
  • #4
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:
 
  • #5
Wouldn't vectors 1,3,4,5 be an equally good answer?
 

Related to Choose from the following set of vectors in R4

What is a vector in R4?

A vector in R4 is a mathematical object that represents a quantity with both magnitude and direction in a four-dimensional space. It is typically denoted as an ordered set of four numbers within parentheses, such as (x, y, z, w).

How do I choose from a set of vectors in R4?

To choose from a set of vectors in R4, you can use various operations such as addition, subtraction, and scalar multiplication to manipulate the vectors and find the desired combination. You can also use geometric interpretations, such as finding the angle between vectors, to help with the selection process.

What is the significance of R4 in vector operations?

R4 is a four-dimensional vector space, which means that it has four independent directions in which a vector can vary. This allows for more complex and diverse vector operations to be performed, making R4 a useful tool in many scientific and mathematical applications.

Can I perform operations on vectors in R4 using a computer program?

Yes, you can perform operations on vectors in R4 using various computer programs, such as MATLAB, Python, and R. These programs have built-in functions and libraries that allow for easy manipulation and analysis of vectors in R4.

What are some real-world applications of choosing from a set of vectors in R4?

Choosing from a set of vectors in R4 has many practical applications in fields such as physics, engineering, and computer graphics. For example, in physics, R4 vectors are used to model the motion of objects in 4D space, while in computer graphics, they are used to represent 3D objects in 4D space for animation and visualization purposes.

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