If \(\begin{bmatrix}x & y & z\\ 2 & u & v\\ -1 & 6 & w\end{bmatrix}\) is skew symmetric matrix, then value of \(x^2 + y^2 + z^2 + u^2 + v^2 + w^2\) is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 41
In a skew symmetric matrix, \(a_{ij} = -a_{ji}\). So every diagonal element is 0, and each element above the diagonal is the negative of its mirror element below it.
Diagonal elements:
\(x = 0,\quad u = 0,\quad w = 0\)
Elements above the diagonal:
\(y = -a_{21} = -2\)
\(z = -a_{31} = 1\)
\(v = -a_{32} = -6\)
Hence
\(x^2 + y^2 + z^2 + u^2 + v^2 + w^2 = 0 + 4 + 1 + 0 + 36 + 0 = 41\)