[[Linear Independence]] is a property of an [[Ordered Set]] of [[Vector|Vectors]]. $\huge \let \vec{v_{1}}, \cdots \vec{v_{m}}\in \R^{n}$ The [[Ordered Set]] $\set{\vec{v_{1}}\cdots \vec{v_{m}}}$ is [[Linear Independence|Linearly Independent]] if the *only* solution to the [[Homogeneous Equation]] created by the [[Linear Combination]] is *only* the [[Trivial Solution]]. If the [[Reduced Row Echelon Form|RREF]] of the [[Augmented Matrix]] from the set has a [[Rank]] equal to $\min\pa{m, n}$ For any [[Ordered Set]] of [[Vector|Vectors]] that is [[Linear Independence|Linearly Independent]], any [[Subset]] is also [[Linear Independence|Linearly Independent]]