> [!NOTE] Definiton > Let $V$ be a [[Real Vector Space|real vector space]]. Let $L \subset V$ be a [[Subsets|subset]]. Then $L$ is linearly independent iff for all $s\geq 1,$ $v_{1},v_{2},\dots,v_{s}\in L$ and $\lambda_{1},\dots,\lambda_{s}\in \mathbb{R}$ $\lambda_{1}v_{1}+\lambda_{2}v_{2}+\dots+\lambda_{s}v_{s}=0_{V} \implies \lambda_{1}=\lambda_{2}=\dots=\lambda_{s}.$ **Note**: Negation gives that $L$ is linearly dependent iff there exist $s\geq 1,$ $v_{1},v_{2},\dots,v_{s}\in L$ and $\lambda_{1}v_{1}+\lambda_{2}v_{2}+\dots\lambda_{s}v_{s}=0_{V}$ and for some $i=1,2,\dots,s,$ $\lambda_{i}\neq 0.$