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Superset of Linearly Dependent Set is Linearly Dependent

Last updated Nov 1, 2022

# Statement

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

# Proof

Use the same finite Linear Combination that makes $S$ Linearly Dependent for $R$. $\square$