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Subset of Linearly Independent Set is Linearly Independent

Last updated Nov 1, 2022

# Statement

Let $V$ be a Vector Space and let $S \subset V$ be Linearly Independent. Then for all $R \subset S$, $R$ is Linearly Independent.

# Proof

If not, then $S$ would be Linearly Dependent by Superset of Linearly Dependent Set is Linearly Dependent