Mathematics — Linear Algebra · linear-dependence-scalar-multiple
Problem
Suppose that V is a vector space and u,v∈V are two vectors in V. Use the definition of linear independence to prove that S={u,v} is a linearly dependent set if and only if one of the two vectors is a scalar multiple of the other. Prove this directly in the context of an abstract vector space (V), without simply giving an upgraded version of Theorem DLDS for the special case of just two vectors.