# linear algebra

posted by
**chris**
.

show that if u (dot) v = 0 for all vectors v, then u = 0.

One of the Axioms an inner product has to satisfy is:

x dot x >=0 where equality only holds if x = 0

So, in your problem you take the special case v = u. Then:

u dot u = 0 ---->

u = 0