Superset of Linearly Dependent Set is Linearly Dependent

Theorem
Any set containing a linearly dependent set is also linearly dependent.

Proof
Follows directly from Subset of Linearly Independent Set:

Suppose $$\left\{{a_1, a_2, \ldots, a_n}\right\}$$ is a linearly independent set.

Then any subset $$\left\{{b_1, b_2, \ldots, b_m}\right\}$$ of $$\left\{{a_1, a_2, \ldots, a_n}\right\}$$ must itself be linearly independent.

Thus if $$\left\{{b_1, b_2, \ldots, b_m}\right\}$$ is linearly dependent, then so must $$\left\{{a_1, a_2, \ldots, a_n}\right\}$$ be.