The number of non-trivial solutions of the system x-y+z=0, x+2 y-z=0, 2 x+y+3 z=0 is

Step-by-step solution

Write given system of equations in matrix form A X=B . [ array ccc 1 & -1 & 1 1 & 2 & -1 2 & 1 & 3 array ] [ array l x y z array ]= [ array l 0 0 0 array ] Now, aligned & |A|= | array ccc 1 & -1 & 1 1 & 2 & -1 2 & 1 & 3 array | & =1(6+1)+1(3+2)+1(1-4) & =7+5-3 & =9 0 aligned Since, |A| 0 . So, the given system of equations has only trivial solution. So, there is no non-trivial solution.