Originally Posted by
Nora314 If you have 4 vectors: u = [3, 2, -4] v = [-6, 1, 7] w = [0, -5, 2] z = [3, 7, -5]
and the sets {u, v}, {u, w}, {u, z}, {v, w}, {v, z}, and {w, z} are all linearly independent, than why can we not assume that the set {u, v, w, z} is linearly independent as well?
Because, there is a theorem that says that a set is linearly dependent if at least one of the vectors is a combination of the others, so if we try all of the combinations, and none of the vectors are a combination of the others, than why can we not assume that {u, v, w, z} is linearly independent?