Let v1 v2 v3 be linearly independent vectors in vector space

Let {v₁, v₂, v₃} be linearly independent vectors in vector space V. Is the set {v₂-v₃, v₁-v₂, v₃-v₁} linearly dependent or independent?

Solution

Since 1(v₂ – v₃)+1(v₁ – v₂)+1( v₃ – v₁ ) = 0, therefore, by the definition of linear dependence, the set {v₂-v₃, v₁-v₂, v₃-v₁} is linearly dependent