\title	{Cálculo de cij en la matriz producto 3x3}
\author	{XIAO Gang}
\email	{xiao@unice.fr}
\format	{html}
\computeanswer{yes}

\integer{s=3}
\text{random=random}
\matrix{A=pari(print(matrix(\s,\s,x,y,if(x>y,tz,(\random(9)+1)*(2*\random(2)-1)))))}
\matrix{B=pari(print(matrix(\s,\s,x,y,if(x<y,tz,(\random(9)+1)*(2*\random(2)-1)))))}
\text{sh1=shuffle(\s)}
\text{sh2=shuffle(\s)}
\text{sh3=shuffle(\s)}
\text{sh4=shuffle(\s)}
\matrix{A=pari(print(vecextract([\A],[\sh1],[\sh2])))}
\matrix{B=pari(print(vecextract([\B],[\sh3],[\sh4])))}
\text{AT=wims(texmath [\A])}
\text{BT=wims(texmath [\B])}
\text{AT=wims(replace internal tz by ? in \AT)}
\text{BT=wims(replace internal tz by ? in \BT)}
\text{CT=wims(texmath [c11,c12,c13;c21,c22,c23;c31,c32,c33])}
\text{i=wims(positionof item 1 in \sh1)}
\text{j=wims(positionof item 1 in \sh4)}
\text{good=c\i\j}
\integer{c=pari(([\A]*[\B])[\i,\j])}
\steps{
reply 1
reply 2}

\statement{Tenemos el siguiente producto de matrices \s&times;\s, donde el 
signo de interrogación representa los elementos desconocidos.
<p><center>
 \(\AT\BT = \CT)
</center> <p>
\if{\step=1}{
 Paso 1. Solo hay un elemento determinable en la matriz producto.
 Es \embed{reply 1,4}. <br>
 (Por ejemplo, <tt>c11</tt> para \(c11).)
}{
 Paso 2. El elemento determinable es \(c\i\j) = \embed{reply 2,6}.
}}

\answer{El elemento determinable es}{\good}{type=atext}
\answer{c\i\j}{\c}{type=number}
