# linear dependence on $\mathbb R^n$

$S_1$ and $S_2$ finite sets on $\mathbb{R}^n$, $S_1$ is a subset of $S_2$, $(S_1\neq S_2)$. If $S_2$ is linearly dependent, so:

$S_1$ could be linearly dependent?

$S_1$ Could be linearly independent?

How can i answer this, and show some examples?

-
Welcome to Math.SE! We use Mathjax here (e.g. $\theta$ for $\theta$): meta.math.stackexchange.com/questions/5020/…. If this is homework or revision, please say so with a tag. It's best if you show your working so far too :) –  Alice Nov 19 '13 at 19:13
@BrettFrankel : Your summary said you fixed a typo (although it was unclear what that was) but you left all the other typos intact, and prevent me from being able to save my edit that fixed them. –  Michael Hardy Nov 19 '13 at 19:26
@MichaelHardy My mistake. I was "improving" another user's edit by removing the TeX markup that he/she added to the title, and evidently overlooked the issues in the body of the post. –  Brett Frankel Nov 19 '13 at 19:32

You can have both of them. For example suppose $S_{2}=\lbrace e_{1} , \ldots, e_{n} , e_{1} + e_{2} \rbrace$. If you have $S_{1}= \lbrace e_{1} , \ldots , e_{n} \rbrace$, it is linear independent. On the other hand you can have $S_{1} = \lbrace e_{1} , e_{2} , e_{1} + e_{2} \rbrace$. So there is no generic answer.