# Linear Independence

Let $B={v_{1},…,v_{k}}$ be a set of vectors in $R_{n}$. We say that $B$ is linearly dependent if there exist $c_{1},...,c_{k}∈R$, not all zero, so that $c_{1}v_{1}+⋯+c_{k}v_{k}=0$

We say that $B$ is linearly independent if the only solution to
$c_{1}v_{1}+⋯+c_{k}v_{k}=0$ is $c_{1}=⋯=c_{k}=0$, which we call the *trivial solution*.