Let B = \left(\begin{array}{c|ccc} 1 & 0 & ... & 0 \\\hline 0 & & & \\ \vdots & & B' & \\ 0 & & & \end{array}\right) ,
where B' is an mxn submatrix of B.
How do I prove the following:
If rank(B) = r, then rank(B') = r - 1.
Any help is appreciated. thanks.