\title	{Invertibilidad triangular 3x3}
\author	{XIAO Gang}
\email	{xiao@unice.fr}
\format	{html}

\text{inv=invertible}
\text{yes=Siempre \inv}
\text{no=Nunca \inv}
\text{dep=Depende de \(t)}
\text{bad=\yes,\no,\dep}
\integer{ch=random(1,2,3)}
\text{bt=random(t,-t,2t,-2t,t^2,-t^2,t^2+1,t^2+2,t^2+3,t^2-1,t^2-2,t+1,t-1,1-t)}
\text{at=0}
\if{\ch=1}{
 \text{good=\yes}
 \if{random(1,1,1,2,2)=1}{
  \text{tt=random(4,5,6)}
 }{
  \text{tt=random(1,2)=1?random(1,2,3),random(4,5,6):random(1,2,3)}
  \text{at=randint(1..8)*t^2+randint(1..8)}
 }
}
\if{\ch=2}{
 \text{good=\no}
 \text{tt=random(1,2,3),random(4,5,6)}
}
\if{\ch=3}{
 \text{good=\dep}
 \text{tt=random(1,2)=1?random(1,2,3),random(4,5,6):random(1,2,3)}
 \text{at=random(t,-t,2t,-2t,t^2,-t^2,t^2-1,t^2-2,1-t^2,2-t^2,t+1,t-1,1-t)}
}
\text{a1=\at}
\text{a2=\at}
\text{a3=\at}
\text{a4=\bt}
\text{a5=\bt}
\text{a6=\bt}

\integer{range=20}
\integer{a1=1 notitemof \tt?random(1..\range)*random(-1,1)}
\integer{a2=2 notitemof \tt?random(1..\range)*random(-1,1)}
\integer{a3=3 notitemof \tt?random(1..\range)*random(-1,1)}
\integer{a4=4 notitemof \tt?random(1..\range)*random(-1,1)}
\integer{a5=5 notitemof \tt?random(1..\range)*random(-1,1)}
\integer{a6=6 notitemof \tt?random(1..\range)*random(-1,1)}
\text{A=random(1,2)=1?\a1,\a4,\a5;0,\a2,\a6;0,0,\a3:
 \a1,0,0;\a4,\a2,0;\a5,\a6,\a3}

\statement{Determine en qué condiciones la siguiente matriz es invertible, siendo
\(t) un número real.
<p><center>
 \([\A])
</center><p>
}

\choice{La respuesta}{\good}{\bad}