Originally Posted by

**Runty** The main issue I'm having with this question is the term "abstract vector space". It hasn't popped up in our course material, and I'm sure the adjective "abstract" changes the meaning significantly. Here's the question:

Let $\displaystyle V$ be an abstract vector space. If u, v and w are linearly independent vectors in $\displaystyle V$ determine which, if any of the following sets are linearly independent:

$\displaystyle S_1=\{u,u+v,v+w,w\}$

$\displaystyle S_2=\{u,u+v,u-v,v+w\}$

$\displaystyle S_3=\{u,u+v,u-v+w\}$

In each case, justify your conclusions.

I'm under the assumption that none of these sets are linearly independent, since in each case the set has at least one linearly dependent vector (usually dependent on the first vector). But considering the addition of the word "abstract", I have to question whether my assumption is correct.