The value of $Δ=\begin{vmatrix}1 & 1+ac & 1+bc\\1 & 1+ad & 1+bd\\1 & 1+ae & 1+be\end{vmatrix},$ is

0

The correct answer is option (2) : 0

We have,

$Δ=\begin{vmatrix}1 & 1+ac & 1+bc\\1 & 1+ad & 1+bd\\1 & 1+ae & 1+be\end{vmatrix}$

$⇒Δ=\begin{vmatrix}1 & ac & bc\\1 & ad & bd\\1 & ae & be\end{vmatrix}$  [Applying $C_2→C_2-C_1, C_3→C_3-C_1$]

$⇒Δ=ab\begin{vmatrix}1 & c & c\\1 & d & d\\1 & e & e\end{vmatrix}$ [Taking a and b common from $C_2$ and $C_3$ respectively]

$⇒Δ=0$