You are Here: Home >< Maths

# Vectors and linear dependence Watch

1. Show vectors (0,3,1-1) (6,0,5,1) (4,-7,1,3) form a linearly dependent set in "R^4"

Does this just mean show the vectors are linearly dependent as I know how to do that, its just the R^4 thats confusing me.

Also which of the following vectors form a basis for R^3?
(1,0,0) (2,2,0) (3,3,3)

(3,1,-4) (2,5,6) (1,4,8)

Is this again just asking which of the vectors are a linearly dependent? I would probably know how to work it out, I just can't get my head around the wording of the question, so I'm not sure what they are asking?
2. Also find the vector v for the basis S=(v1,v2,v3)

v=(2,-1,3)
v1=(1,0,0)
v2=(2,2,0)
v3=(3,3,3)

Any help on to approach this question would be appreciated, im not really sure what Im meant to be looking for here. Isn't the vector v already given?
3. (Original post by Gorrilaz)
Show vectors (0,3,1-1) (6,0,5,1) (4,-7,1,3) form a linearly dependent set in "R^4"

Does this just mean show the vectors are linearly dependent as I know how to do that, its just the R^4 thats confusing me.

Yes, you only need to show the vectors are linearly dependent. is simply the vector space concerned.

(Original post by Gorrilaz)
Also which of the following vectors form a basis for R^3?
(1,0,0) (2,2,0) (3,3,3)

(3,1,-4) (2,5,6) (1,4,8)

Is this again just asking which of the vectors are a linearly dependent? I would probably know how to work it out, I just can't get my head around the wording of the question, so I'm not sure what they are asking?
No. To show that vectors from a basis for a space, you have to show (a) that they form a linearly independent set and (b) that they span the vector space ( in this case)

Hint: since is a three dimensional space, there will be only three vectors in the basis
4. (Original post by Gorrilaz)
Also find the vector v for the basis S=(v1,v2,v3)

v=(2,-1,3)
v1=(1,0,0)
v2=(2,2,0)
v3=(3,3,3)

Any help on to approach this question would be appreciated, im not really sure what Im meant to be looking for here. Isn't the vector v already given?
If (v1, v2, v3 ) is a basis then

It means 3 scalar equations . Solve these simoultaneously for

Another method would be the base transformation.

Updated: May 7, 2012
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

It's a dilemma

Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups
Study resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.