A little confused with this concept, how do you know if a set of vectors is linearly independent or not? Been reading my textbook and it doesn't really make sense to me. So for example I have these questions?

P = {(2, 1), (1, 2), (3, 3)}

Q = {(2, 1), (1, 2)}

S = {(3, 5, 7), (4, 6, 8)}

How do I know if they're linearly independent or not?