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

\integer{range=10}
\integer{half=\range/2}
\integer{sense=random(1,2)}
\text{s=item(\sense,s,t)}
\text{t=item(\sense,t,s)}
\integer{sval=random(-\range..\range)}
\integer{tval=random(-\range..\range)}
\matrix{mat=randint(-\range..\range),2*randint(-\half..\half)+1,2*randint(-\half..\half)
randint(-\range..\range),\s,2*randint(-\half..\half)+1
\t,randint(-\range..\range),randint(-\range..\range)}
\text{sh=shuffle(3)}
\matrix{mat=random(1,2)=1?pari(print(vecextract([\mat],[\sh],[\sh]))):
	pari(print(vecextract([\mat]~,[\sh],[\sh])))}
\text{mat1=wims(replace internal s by \sval in \mat)}
\text{mat1=wims(replace internal t by \tval in \mat1)}
\integer{trace=pari(trace([\mat1]))}
\integer{deter=pari(matdet([\mat1]))}

\statement{Find the values of the parameters \(s) and \(t) such that
the matrix
<center>\(A=[\mat])</center>
verifies det\((A) = \deter) and trace\((A)=\trace).}
\answer	{<i>s</i>}{\sval}
\answer {<i>t</i>}{\tval} 

