My Math Forum Subset of S

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 March 11th, 2009, 08:44 PM #1 Newbie   Joined: Feb 2009 Posts: 18 Thanks: 0 Subset of S S={v1=[-4 v2=[7 v3=[-3 v4=[-6 v5=[1 } -2 1 3 -6 3 -1 -2 0 -1 4 4 -6 2 -2 -2 7] -8] 4] 3] -6] How can I find two subsets of S, each with more than one element, that are linearly independent.Justify your answer.
 March 16th, 2009, 07:42 AM #2 Newbie   Joined: Mar 2009 Posts: 21 Thanks: 0 Re: Subset of S Let's start with $v_1$. Clearly, $\{v_1\}$ is linearly independent. Now, is $\{v_1,v_2\}$ linearly independent? To check, we see if $av_1+bv_2=0$ implies $a=b=0$. As a matter of fact, it does (verify it). Therefore, $\{v_1,v_2\}$ is a linearly independent subset of $S$. Similarly, you can show that $\{v_1,v_3\}$ is a linearly independent subset of $S$.

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