\title	{Rank and multiplication}
\author	{XIAO Gang}
\email	{xiao@unice.fr}
\format	{html}

\integer{rank=random(3..7)}
\integer{m=random(\rank+1..15)}
\integer{n=random(\rank+2..15)}

\statement{Let C be a matrix of size \m&times;\n, of rank \rank.
What is the condition on <i>n</i>, in order that there exist a
matrix A of size \m&times;<i>n</i> and a matrix B of size
<i>n</i>&times;\n, such that C=AB&nbsp;?}
\choice {The condition} {<i>n</i> is more than or equal to c}
	{<i>n</i> is less than or equal to c}
\answer	{Where c}  {\rank}
\choice {This condition is} {necessary and sufficient}
	{necessary but not sufficient, sufficient but not necessary}

