Explanation The first two vectors (u₁ and u₂) look hopeless from the point of view of quick computation by hand. But u₃ and u₄ are highly patterned (human beings are supposed to recognize patterns!). We can take advantage of the patterns and realize that u₃+2u₄=0. This is a non-trivial linear combination of the elements of the set {u₁, u₂, u₃, u₄} (the coefficients of u₁ and u₂ are both 0). Therefore the set {u₁, u₂, u₃, u₄} is linearly dependent.