Proof:
Let S ⊆ V be a subset of a vector space V over F. We have that S
is linearly dependent if and only if there exist vectors v1, v2, .
. . , vn ∈ S such that vi is a linear combination of v1, v2, . . .
, vi−1, vi+1, . . . , vn for some 1 ≤ i ≤ n.