If $\begin{bmatrix}0 & x+y & x+z\\4 & 0 & y+z\\3 & 5 & 0 \end{bmatrix}$ is a skew symmetric matrix, then the value of $(x, y, z)$ is :

(-1, -3, -2)

The correct answer is Option (1) → (-1, -3, -2)

$A^T=-A$   [A = Skew Symmetric]

$∴\begin{bmatrix}0&4&3\\x+y & 0&5\\x+z&y+z&0\end{bmatrix}=\begin{bmatrix}0 & -(x+y) & -(x+z)\\-4 & 0 & -(y+z)\\-3 & -5 & 0 \end{bmatrix}$

$⇒x+y=-4$   ...(1)

$x+z=-3$   ...(2)

$y+z=-5$   ...(5)

Subtracting (3) from (2),

$⇒x-y=2$   ...(4)

Add (1) and (4),

$2x=2$

$⇒x=-1,y=-3,z=-2$