If $\omega $ is a non-real cube root of unity, then
$Δ=\begin{vmatrix}a_1+b_1ω & a_1ω^2+b_1 & a_1+b_1ω+c_1ω^2\\a_2+b_2ω & a_2ω^2+b_2 & a_2+b_2ω+c_2ω^2\\a_3+b_3ω & a_3ω^2+b_3 & a_3+b_3ω+c_3ω^2\end{vmatrix}$ is equal to
Answer & explanation
Correct answer: option 2
The correct answer is option (2) : 0
Applying $C_2→C_2 (ω), $ we get
$Δ=\frac{1}{ω}\begin{vmatrix}a_1+b_1ω & a_1ω^2+b_1 & a_1+b_1ω+c_1ω^2\\a_2+b_2ω & a_2ω^2+b_2 & a_2+b_2ω+c_2ω^2\\a_3+b_3ω & a_3ω^2+b_3 & a_3+b_3ω+c_3ω^2\end{vmatrix}$
$⇒Δ=\frac{1}{ω}×0=0$ $[∵ C_1$ and $C_2 $ are indentical $]$