The value of the determinant $\begin{vmatrix}1 & x & y+z\\1 & y & z+x\\1 & z & x+y \end{vmatrix}$ is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0
$Δ=\begin{vmatrix}1 & x & y+z\\1 & y & z+x\\1 & z & x+y \end{vmatrix}$
$C_3→C_3+C_2$
$Δ=\begin{vmatrix}1 & x & x+y+z\\1 & y & x+y+z\\1 & z & x+y+z\end{vmatrix}=0$
as $C_1$ and $C_3$ are proportional