Proof of linear independence
Prove that the four vectors
in form a linearly dependent set, but any three of them are linearly independent.
, prove that are linearly dependent, but any three of them are linearly independent.
(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.