If $\begin{bmatrix} x-2 & 3 & -2 \\ y & 0 & -4 \\ 2 & z & 0 \end{bmatrix}$ is a skew symmetric matrix, then the value of \( x + y + z \) is

3

The correct answer is Option (4) → 3

For a skew–symmetric matrix, the condition is that the transpose of the matrix equals the negative of the matrix, that is A^T=−A. This means two important things:

1. All diagonal elements must be zero.

2. Elements symmetric about the main diagonal are negatives of each other.

Given matrix:

$\begin{bmatrix} x-2 & 3 & -2 \\ y & 0 & -4 \\ 2 & z & 0 \end{bmatrix}$ is a skew symmetric matrix, then the value of \( x + y + z \)

First, diagonal elements must be zero. So x−2=0 ⇒ x=2

Next, compare symmetric positions:

• Element (1,2) = 3, so element (2,1) = y=−3

• Element (1,3) = -2, so element (3,1) must be 2, which already matches.

• Element (2,3) = -4, so element (3,2) = z = 4

  Now find x+y+z = 2+(−3)+4 =3