1. Linear dependence

Let u and v be distinct vectors in a vector space V show that {u,v} is linearly dependant if and only if u or v is a multiple of the other.

A set of vectors are linearly dependent if vectors $v_1 , v_2, ... v_n$ satisfy $a_1 v_1 + a_2 v_2 + ...a_n v_n=0$ where a_i is a scalar and the set of scalars are not all 0.