A linear transformation L: VW is said to be one-to-one if L(V₁) = L(V₂) implies that V₁ = V₂ (i.e., no two distinct vectors V₁, V₂ in V get mapped into the same vector w ∈ W). Show that L is one-to-one if and only if ker(L) = {0ᵥ}.