If $xyz = – 2007$ and $Δ =\begin{vmatrix}a+x&b&c\\a&b+y&c\\a&b&c+z\end{vmatrix}= 0$, then value of $ayz + bzx + cxy$ is
Answer & explanation
Correct answer: option 1
$R_2 → R_2 – R_3, R_1 → R_1 – R_2$
$\begin{vmatrix}x&-y&0\\0&y&-z\\a&b&c+z\end{vmatrix}=0$
$⇒x(cy + yz + bz) + y (az) = 0$
$cxy + xyz + bzx + ayz = 0$
$cxy + bzx + ayz = -2007$