Question

Given this vectorial subspace in R4 generated by these vectors:
V=< (0, 0, 0, 1), (0, 0, 1, 2), (1, 2, 3, 4)>
Provide the base for it

Answer 1

@FSU

Answer 2

tbh im not sure

Answer 3

@blake007

Answer 4

@iGreen

Answer 5

ow :(

Answer 6

@saifoo.khan please help?

Answer 7

base, or basis?

Answer 8

basis i believe

Answer 9

sorry I speak spanish so I get troubles with translating

Answer 10

a basis is a minimum set of linearly independant column vectors that provides a way to approach all the vectors in the the subspace.

does that make sense as a definition?

Answer 11

yes, I believe I need three vectors that are a system generator i think and also linearly independent?

Answer 12

correct

Answer 13

I'm just not sure how to approach he problem in order to obtain those three vectors I was trying to do just elimination in a matrix but i couldnt

Answer 14

echelon comes to mind but im not quite sure if we are given row vectors or column vectors at the moment.

quite frankly, i recall doing something like seting up the matrix A = v1, v2, v3 and getting it into row echelon form

Answer 15

I got a another group of vectors and i used them as rows didnt know they had to specify

Answer 16

it does not specify if its row or column , can i use it as i wish?

Answer 17

thats the part i cant recall at the moment :)

last one a worked on said something to the effect:

v1, v2, v3 form a basis of a subspace if for some abc consants

av1 + bv2 + cv3 = 0 is not the trivial solution, a=b=c=0

Answer 18

so thats a (0,0,0,1) + b (0,0,1,2) + c(1,2,3,4) =0 ?

Answer 19

yes

Answer 20

let me review for a moment to make sure my memory isnt failing me on this point

Answer 21

sure, no problem

Answer 22

av1 + bv2 + cv3 = 0 is ONLY the trivial case.

for example, in R^3 we have the basis

v1 = 001
v2 = 010
v3 = 100

the only way a linear combination of these vectors add up to 0 is if a=b=c=0

Answer 23

this is R^4

Answer 24

it applies to any vector space, now my question is, are we spose to create the basis using the vectors in V only, or are we to create it a basis that can obtian at least the vectors that are in V

Answer 25

http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi

well ill be, theres a webpage i just found that walks you thru it

Answer 26

is asking only to find a basis or the vectorial space

Answer 27

oh wow thanks ! :D

Answer 28

it cleared up my concerns thats for sure.

i knew your set V was linearly independant, i echeloned it, and was of the impression that the vectors themselves formed the basis they wanted.

Answer 29

I cannot use those vectors as the basis you mean?

Answer 30

i thought that was linking to the page i worked out, its this one one the ment

it turns out that v1,v2,v3 form the basis itself

Answer 31

thank you.

Answer 32

youre welcome