Either prove or give a counterexample to the following state

Either prove or give a counterexample to the following statement: If u_1, u_2, u_3 are three vectors in R^3 none of which is a scalar multiple of another, then the set {u_1, u_2, u_3} is linearly independent.

Solution

Let u₁=(1,1,1), u₂=(-1,-2,-3) and u₃=(2,3,4)

Here none of the above three vectors u₁=(1,1,1), u₂=(-1,-2,-3) and u₃=(2,3,4) are a scalar multiple of other

but  u₁ - u₂= u_{3 So, therefore these three vectors are not independent}