Let U be a subspace of ℝn. Show that if u[itex]\in[/itex]U[itex]\bigcap[/itex]U[itex]\bot[/itex], then u=0.
The Attempt at a Solution
I know that U[itex]\bot[/itex] will be orthogonal to U, so any vector u in U dotted with any vector in U[itex]\bot[/itex] will equal 0. But that does not necessarily mean that u = 0 so I must prove something else. I don't know where to include the intersect into all of this, we have never used that kind of thing before.