The greatest value of ‘c’, c∈Rfor which the system of linear equations x−cy−cz=0, cx−y+cz=0, cx+cy−z=0 has a non-trivial solution is

The given homogeneous system has a non-trivial solution⇒Δ=0⇒1-c-cc-1ccc-1=0⇒11-c2+c-c-c2-cc2+c=0⇒2c3+3c2-1=0⇒(c+1)2(c-1/2)=0⇒c=−1,1/2⇒the greatest value of c=1/2