No. Try to find a counterexample (this is possible in R^2).1. The problem statement, all variables and given/known data
If u1 and u2, u2 and u3, u1 and u3 are Linearly Independent, does it follow that {u1,u2,u3} is Linearly Independent?
Oops, can't believe I missed such a simple counter-example.No. Try to find a counterexample (this is possible in R^2).
No. Try to find a counterexample (this is possible in R^2).
You can try thinking about the orthogonal standard basis vectors.I could not find a counter example. I think it is LI.