If ω is cube root of unity and x+y+z=a,   x+ωy+ω2z=b, x+ω2y+ωz=c then which of the following is correct

The determinant of the coefficient matrix is Δ=1111ωω21ω2ω=1ω2-ω4-1ω-ω2+1ω2-ω=3ω2-ω ∵ω4=ω Also Δ1=a11bωω2cω2ω=aω2-ω4-bω-ω2+cω2-ω=a+b+cω2-ω            Δ2=1a11bω21cω=1bω-cω2-1aω-c+1aω2-cb=a+bω2+cωω2-ω    and Δ3=11a1ωb1ω2c=1cω-bω2-1c-aω2+1b-aω=a+bω+cω2ω2-ω ∴By Crammar's rule we have, x=Δ1Δ,y=Δ2Δand z=Δ3Δ. ⇒x=a+b+c3, y=a+bω2+cω3 and z=a+bω+cω23