Are These Vectors Linearly Independent?

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Homework Help Overview

The problem involves determining the linear independence or dependence of a set of vectors S={r,u,d,x}, given that x=4r+4u+4d. Participants are tasked with identifying whether a non-trivial linear relation exists among these vectors.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants express uncertainty about how to start the problem and discuss the setup of a linear combination involving the vectors. There is a focus on identifying the scalar that should be associated with vector x and the implications of the coefficients in relation to linear dependence.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the problem. Some have suggested specific values for the scalar associated with x, while others are questioning the algebraic manipulations involved in establishing linear dependence.

Contextual Notes

Participants note that they are not provided with specific vectors, only scalars, which adds to the complexity of determining the relationship among the vectors. There is also mention of the conditions for linear dependence and independence, focusing on the significance of non-trivial scalars.

halo31
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Homework Statement



Let S={r,u,d,x} be a set of vectors.
If x=4r+4u+4d, determine whether or not the four vectors listed above are linearly independent or linearly dependent. If is dependent, find a non-trivial linear relation.

Homework Equations





The Attempt at a Solution



I don't really know how to start the problem. But I tried to set it up this way.
Let 0=4r-4d-4u+x. In order to make it zero would the scalar of x have to be
1? but I am really lost with lost with problem. Any help would great
 
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halo31 said:

Homework Statement



Let S={r,u,d,x} be a set of vectors.
If x=4r+4u+4d, determine whether or not the four vectors listed above are linearly independent or linearly dependent. If is dependent, find a non-trivial linear relation.

Homework Equations





The Attempt at a Solution



I don't really know how to start the problem. But I tried to set it up this way.
Let 0=4r-4d-4u+x. In order to make it zero would the scalar of x have to be
1? but I am really lost with lost with problem. Any help would great

You've already written 0 as a linear combination of the vectors {r,u,d,x}. Doesn't that mean you are done??
 
well I first have to figure out if its linear dependent or linear independent. I am not given any vectors, just scalars. I am supposed to figure out what scalar number goes in front of the x vector. What I do know when its linear dependent is when there is atleast one nontrivial scalar and when its linear independent is when all scalars are zero. But how do I go about finding what scalar fits in front of the scalar?oh wait wouldn't it be linear dependent since the scalars(4) in front of vectors r,d,u are 4?
 
halo31 said:
well I first have to figure out if its linear dependent or linear independent. I am not give any vectors, just scalars. I am supposed to figure out what scalar number goes in front of the x vector.

You are overthinking this. Try putting 1 in front of x.
 
That I tried. All I know if I divide it I'm left with the same equation as I started with.
 
halo31 said:
That I tried. All I know if I divide it I'm left with the same equation as I started with.

Mmm. I just noticed your algebra is a bit off. If you do it right you have 0=-4*r-4*d-4*u+1*x. All of the scalars in front of the vectors are nonzero and the sum is 0. Linearly dependent or independent??
 
ok thanks
 

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