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
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 3
In a skew symmetric matrix, \(a_{ji} = -a_{ij}\); in particular every diagonal entry is 0.
\(a_{11} = 0\): \(x - 2 = 0\), so \(x = 2\)
\(a_{21} = -a_{12}\): \(y = -3\)
\(a_{32} = -a_{23}\): \(z = -(-4) = 4\)
Also \(a_{31} = 2 = -a_{13}\), as it should be.
\(x + y + z = 2 - 3 + 4 = 3\)