Let $V$ be a [[vector space]] over the [[field]] $K$, and let $\boldsymbol v_{1}, \ldots,\boldsymbol v_{n}$ be [[elements]] of $V$. We shall say that $\boldsymbol v_{1}, \ldots, \boldsymbol v_{n}$ are linearly dependent over $K$ if there exist elements $a_{1}, \ldots, a_{n}$ in $K$ not all equal to 0 such that $ a_{1} v_{1}+\cdots+a_{n} v_{n}=O \quad \exists i :a_i\neq0 $ More informally, if you can form an [[additive inverse]] to one of the vectors by only using the others, then the [[set]] of vectors is not one of [[linearly independent vectors]]