Are These Vectors Linearly Independent?

[halo31]

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

 

[Dick]

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??

 

[halo31]

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?

 

[Dick]

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.

 

[halo31]

That I tried. All I know if I divide it I'm left with the same equation as I started with.

 

[Dick]

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??

 

[halo31]

ok thanks