let v be a vector space over a field of characteristic not equal to two. (a) let u and v be distinct vectors in v. prove that {u, v} is linearly independent if and only if {u v, u − v} is linearly independent. (b) let u, v, and w be distinct vectors in v. prove that {u, v, w} is linearly independent if and only if {u v, u w, v w} is linearly independent.