After lots of work I discovered that the equation $B^T \cdot x = 0$ has non-trivial solution, I want to conclude that also $B \cdot x = 0$ has non-trivial solution but I can't find a way to prove it.

Any help will help :) thanks

(And sorry about that I don't know latex or the math format you are using here)

edit: B is from the order **n x m**