Vectors and linear dependence
Maths and statistics discussion, revision, exam and homework help.
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Vectors and linear dependenceShow 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? -
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Re: Vectors and linear dependenceAlso 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? -
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Re: Vectors and linear dependence(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.
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 ((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?
in this case)
Hint: since is a three dimensional space, there will be only three vectors in the basis
Last edited by Plato's Trousers; 07-05-2012 at 10:23. -
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Re: Vectors and linear dependenceIf (v1, v2, v3 ) is a basis then(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?
It means 3 scalar equations . Solve these simoultaneously for
Another method would be the base transformation.
