\title{Combinación lineal}
\language{en}
\range{-5..5}
\author{Gang XIAO}
\email{xiao@unice.fr}
\computeanswer{no}
\format{html}
\precision{1000000}

\integer{c11=random(2..10)*random(-1,1)}
\integer{c12=random(2..10)*random(-1,1)}
\integer{c13=random(2..10)*random(-1,1)}
\integer{c14=random(2..10)*random(-1,1)}
\integer{c21=random(2..10)*random(-1,1)}
\integer{c22=random(2..10)*random(-1,1)}
\integer{c23=random(2..10)*random(-1,1)}
\integer{c24=random(2..10)*random(-1,1)}
\integer{c31=random(2..10)*random(-1,1)}
\integer{c32=random(2..10)*random(-1,1)}
\integer{c33=random(2..10)*random(-1,1)}
\integer{c34=random(2..10)*random(-1,1)}

\statement{Tenemos 4 vectores del espacio:
<p><center>
 v<sub>1</sub> = (\c11,\c21,\c31) ,
 v<sub>2</sub> = (\c12,\c22,\c32) ,
 v<sub>3</sub> = (\c13,\c23,\c33) ,
 v<sub>4</sub> = (\c14,\c24,\c34) .
</center> <p>

Hallar 4 enteros a,b,c,d tal que
<p><center>
	a v<sub>1</sub> + b v<sub>2</sub> + c v<sub>3</sub> + d
	v<sub>4</sub> = 0 ,
</center> <p>
con la condición de que  los enteros a,b,c,d no sean todos nulos.
}

\answer{a}{\sx}
\answer{b}{\sy}
\answer{c}{\sz}
\answer{d}{\st}

\condition{a,b,c son enteros y no todos nulos}
{
abs(\sx)+abs(\sy)+abs(\sz)+abs(\st)>0 and
abs(round(\sx)-(\sx))<=0 and
abs(round(\sy)-(\sy))<=0 and
abs(round(\sz)-(\sz))<=0 and
abs(round(\st)-(\st))<=0
}

\condition{La suma algebraica de los vectores es cero}
{
(\c11)*(\sx)+(\c12)*(\sy)+(\c13)*(\sz)+(\c14)*(\st)=0 and
(\c21)*(\sx)+(\c22)*(\sy)+(\c23)*(\sz)+(\c24)*(\st)=0 and
(\c31)*(\sx)+(\c32)*(\sy)+(\c33)*(\sz)+(\c34)*(\st)=0
}