Linear independence

Definition

A set of vectors $x_1\dots x_n$ are said to be linearly independent if there is no vector in the set that is a linear combination of the others.

$$\sum _{i=1}^n{a}_i{v}_i=0$$

System is linearly independent $⟺$ $\forall a_i=0$.

System if dependent if there exists a linear combination with coefficients different from 0.