Can someone explain me or prove this to me.

It's written in my notebook that we have aReduced row echelon formMatrix and it says that r=The number of rows in the matrix(excluding the rows that have only 0 in it) in other words the rank, i guess. and n=The number of unknowns (in other words x1,x2,x3,....,xn)

And we have the Ax=0 (Homogoneous system), and it says that x ( the solutions) is a subspace, which is understandable, I proved it , however it says that the numbero f vectors in the basis is

n-r. how did it come to this conclusion? Can someone prove this please? Thank you.