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# If the equation $-2x+y+z=i\;;x-2y+z=m\;;x+y-2z=n$ such that $i+m+n=0,$ then the system has

(1) a non-zero unique solution$\;$ (2)trivial solution(3)infinitely many solution $\;$(4)no solution

Can you answer this question?

$-2x+y+z=l$-----(1)
$x-2y+z=m$-----(2)
$x+y-2z=n$-----(3)
$l+m+n=0$-----(4)
$l+m=$-----(5)
(1) +(2) => $-x-y+z=l+m$
$-x-y+2z=-n$ from 5
$x+y-2z=$ =>(3)
no of equations < no of unknowns
Therefore the system is consistent and has infinitely may solutions.
Hence 3 is the correct answer.
answered May 5, 2014 by