Explanation "Everything" is a mess until you notice that u₃ is the 0 vector (all of its entries are 0). So 0u₁+0u₂+(anything)u₃+0u₄=0 is an example of a non-trivial linear combination of u₁, u₂, u₃, and u₄ which is equal to 0 (as long as that anything is non-zero, of course!). So the set {u₁, u₂, u₃, u₄} is not linearly independent.