MHB Choose from the following set of vectors in R4

  • Thread starter Thread starter forzi
  • Start date Start date
  • Tags Tags
    Set Vectors
AI Thread Summary
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
Messages
3
Reaction score
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?
 
Mathematics news on Phys.org
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?
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Thread 'Six Pencil Puzzle'

Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
View full post »

Similar threads

I Desymmetrization of a combinatorial set
Replies
8
Views
2K
I Solving simultaneous vector equations
Replies
11
Views
3K
I Principal difference between complex numbers and 2D vectors revisited
Replies
24
Views
3K
B Why is it Important that something is a vector space?
Replies
10
Views
5K
B Calculating the perfect tennis shot using vectors
Replies
2
Views
2K
I Label propagation equation: what are the terms?
Replies
3
Views
1K
I Vector subspace and basis vectors in the context of data science
Replies
6
Views
3K
A Rich "isotropic tensor" concept
Replies
1
Views
2K
MHB How can we construct the matrix S ?
Replies
8
Views
3K
Is this vector in the image of the matrix?
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top