Problem:

Determine a linearly independent set of vectors that spans the same subspace of V as that spanned by the original set of vectors.

V=R3, {(1,1,1),(1,-1,1),(1,-3,1),(3,1,2)}

Question:

There is a theorem that says, "If one of the vectors in the set is a linear combination of the other vectors in the set, then that vector can be deleted from the given set of vectors".

I found the following dependency relationship among these vectors to be:

v1-2v2+v3=0

Now, I can solve for any one of the vectors in terms of the other two. Does this mean I can remove one, two, or three vectors from the original set, or am I limited to just one "vector removal"?

Thanks for any help!