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