SOLUTION: hello How do i find the basis of a space spanned by a set of vectors v1 = (1,-2,0,0,3),v2=(2,-5,-3,-2,6),v3=(0,5,15,10,0),v4=(2,6,18,8,6). i tried it out assuming that if the sp

Question 378113: hello
How do i find the basis of a space spanned by a set of vectors v1 = (1,-2,0,0,3),v2=(2,-5,-3,-2,6),v3=(0,5,15,10,0),v4=(2,6,18,8,6). i tried it out assuming that if the space is spanned by these vectors then any arbitrary vector in R^5 can be found by a linear combination of these vector right? but i got no solution to an arbitrary vector of (3, 2, 4, 5, 6). if that is the case is it safe to say that no basis exists for a space spanned by v1, v2, v3, v4?
thanks for your help

Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!
If v1,v2,v3,v4 are linearly independent, the space spanned by them is 4 dimensional. It's a subspace of R^5.
If the vi's are linearly independent, they form a generating part of this lower dimensional sub-space (lower equals 3).

RELATED QUESTIONS
1)In 3d-space, let v1=(0,2,1) v2=(2,1,1) v3=(1,3,-1) v4=(4,2,1). Write v4 as linear... (answered by Fombitz)

I have a homework problem that I don't know how to do. I'm asked to solve the following (answered by venugopalramana)

Determine if the vectors v1 = (1,2,3), v2 = (1,0,-1), v3 = (2,2,2), v4 = (2,4,6) span R^3 (answered by ikleyn)

Let S={v1, v2, v3}where v1^T=[1 0] v2^T=[0 1] v3^T=[-1 1] (answered by venugopalramana)

Let v1=[2,0,6] , v2=[-1,4,5] , v3=[1,-1,1]. Find the value(s) of k for which b=[2,1,k]... (answered by ikleyn)

Hi,my name is Natalia. I solved two problems, but I'm not sure that I did it right. I... (answered by venugopalramana)

Let v1= [-1, 4, -2, 2].v2 = [2, -10, 6, -1].v3 = [-7, 26, -14, 23],v4 = [0, -2, 1, 6] (answered by ikleyn)

Show that if s=(v1,v2,v3) is a linearly dependent set of vectors in a vector space V, and (answered by robertb)

This is my second and last question. This is not in a textbook. a.)Let T be a linear... (answered by venugopalramana)