Proof of linear independence

**problem:**

(a)

Prove that the four vectors

in form a linearly dependent set, but any three of them are linearly independent.

(b)

, prove that are linearly dependent, but any three of them are linearly independent.

**attempt:**

(a) To prove that the four vectors are linearly dependent, I guess I could set up four linear equations and solve them.

But I'm thinking it should be enough to show that:

.

The thing I do not understand is the "any three of them are linearly independent" part.

How do I go about proving that without checking all combinations?

(b) . Again, I don't know how to prove the "any three of them" part without checking all combinations.

Thanks!