$ a,b,c\in \Bbb R$
$2x_1+2x_2+3x_3=a$
$3x_1-x_2+5x_3=b$
$x_1-3x_2+2x_3=c$
if a,b and c is a solution of this linear equation system find the relation between a,b and c
I dont understand the question. without knowing a,b and c is a solution of eq.syst. I found
$$ \begin{matrix} 2 & 2 & 3 &a \\ 3 & -1 & 5&b \\ 0 & 0 & 0 &a+c-b\\ \end{matrix} $$
and therefore $b=a+c$
when I use a,b and c as a solution
$2a+2b+3c=a$
$3a-b+5c=b$
$a-3b+2c=c$
reduced row echolon form is
$$ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{matrix} $$
it gives a=0 b=0 c=0