Linear Independence

Let $B=\{v_1,\dots ,v_k\}$ be a set of vectors in ${\mathbb{R}}^n$. We say that $B$ is linearly dependent if there exist $c_1,...,c_k\in \mathbb{R}$, not all zero, so that $c_1{\vec{v}}_1+\cdots +c_k{\vec{v}}_k=\vec{0}$

We say that $B$ is linearly independent if the only solution to $c_1{\vec{v}}_1+\cdots +c_k{\vec{v}}_k=\vec{0}$ is $c_1=\cdots =c_k=0$, which we call the trivial solution.