# Basis of Column Space of matrix that is in Row Reduced Echelon form

I'm considerably new to proving things(and to Linear Algebra too).So, I hope someone would help me with this.

While proving Row Rank of Matrix = Column Rank of Matrix

Proof used the point that

For a Row Reduced Echelon Matrix, Basis of Column Space is just set of columns that contain leading non-zero entries.

Can someone provide a proof of this (Hints would more be appreciated)?

• If you mean the column space of the rref and not the original matrix, this should be pretty obvious. Each such column has a different single nonzero entry that corresponds to a nonzero row of the rref. – amd Feb 25 '18 at 7:42