$\begin{vmatrix} 1 & 2 & 3\\4 & 5 & 6\\7 & 8 & 9\end{vmatrix}= x\begin{vmatrix}2 & 3\\ 8 & 9 \end{vmatrix}+ y \begin{vmatrix} 1 & 3\\7 & 9 \end{vmatrix}+z\begin{vmatrix}1 & 2\\7 & 8\end{vmatrix}$ Then $x+y + z $ is :

-5

The correct answer is Option (3) → -5

$\begin{vmatrix} 1 & 2 & 3\\4 & 5 & 6\\7 & 8 & 9\end{vmatrix}= -4\begin{vmatrix}2 & 3\\ 8 & 9 \end{vmatrix}+ 5 \begin{vmatrix} 1 & 3\\7 & 9 \end{vmatrix}-6\begin{vmatrix}1 & 2\\7 & 8\end{vmatrix}$

on comparison $x=-4,y=5,z=-6$

$x+y+z=-5$