If $ s= a + b +c ,$ then the value of
$Δ=\begin{vmatrix}s+c & a & b\\c & s+a & b\\c & a & s+b\end{vmatrix},$ is
Answer & explanation
Correct answer: option 2
The correct answer is option (2) : $2s^3$
We have,
$Δ=\begin{vmatrix}s+c & a & b\\c & s+a & b\\c & a & s+b\end{vmatrix}$
$⇒Δ=\begin{vmatrix}s+a+b+c & a & b\\s+a+b+c & s+a & b\\s+a+b+c & a & s+b\end{vmatrix}$ [Applying $C_1→C_1+C_2+C_3$]
$⇒Δ= (s+a+b+c)\begin{vmatrix}1 & a & b\\1 & s+a & b\\1 & a & s+b\end{vmatrix}$
$⇒Δ=2s\begin{vmatrix}1 & a & b\\0 & s & 0\\0 & 0 & s\end{vmatrix}$ $\begin{bmatrix} Applying \, R_2 →R-2-R_1\\R_3→R_3-R_1\end{bmatrix}$
$⇒Δ= 2s^3$