\title	{Determinante y rango}
\author	{XIAO Gang}
\email	{xiao@unice.fr}
\format	{html}

\text{Det=det}
\text{Rank=rango}
\integer{size=random(5..20)}
\integer{r2=random(\size/2..\size-1)}
\text{ddd=shuffle(20)}
\integer{det1=item(1,\ddd)*random(-1,1)}
\integer{det2=item(2,\ddd)*random(-1,1)}
\integer{detp=\det1*\det2}

\integer{o=random(1,2)}
\text{A=item(\o,A,B)}
\text{B=item(\o,B,A)}
\text{t1=item(\o,1,2)}
\text{t2=item(\o,2,1)}

\text{detA=\Det(\(\A))=\det1}
\text{detB=\Det(\(\B))=\det2}
\text{detA0=\Det(\(\A))=0}
\text{detB0=\Det(\(\B))=0}
\text{rankA1=\Rank(\(\A))=\size}
\text{rankB1=\Rank(\(\B))=\size}
\text{rankA2=\Rank(\(\A))=\r2}
\text{rankB2=\Rank(\(\B))=\r2}
\text{askrankAB=\Rank(\(AB))}
\text{askdetAB=\Det(\(AB))}
\text{eq==}
\text{ne=&lt;&gt;}
\text{lt=&lt;}
\text{gt=&gt;}

\matrix{data=
\detA,\rankB1,\askrankAB,\eq,\size
\detA,\rankB1,\askdetAB,\ne,0
\detA,\rankB2,\askrankAB,\eq,\r2
\detA,\rankB2,\askdetAB,\eq,0
\detA,\detB,\askrankAB,\eq,\size
\detA0,\rankB1,\askrankAB,\lt,\size
\detA0,\rankB1,\askdetAB,\eq,0
\rankA1,\rankB2,\askrankAB,\eq,\r2
\rankA1,\rankB2,\askdetAB,\eq,0
\detA0,\detB,\askrankAB,\lt,\size
\rankA1,\rankB1,\askdetAB,\ne,0
}

\text{data=randomrow(\data)}
\text{cond1=item(\t1,\data)}
\text{cond2=item(\t2,\data)}
\text{ask=item(3,\data)}
\text{good1=item(4,\data)}
\text{val=item(5,\data)}
\text{bad=\eq,\lt,\gt,\ne}

\statement{Sean \(A) y \(B) dos matrices \size&times;\size, tales que
\cond1 y \cond2. Entonces
<p><center>
\ask \embed{choice 1} \embed{reply 1,5}.
</center> <p>
(Debes colocar la mejor respuesta.)
}

\choice{\ask is}{\good1}{\bad}
\reply{the value}{\val}
