If \(A = \begin{bmatrix} 0 & 2 & -3 \\ y & 0 & -1 \\ z & x & 0 \end{bmatrix}\) is skew symmetric matrix, then \(x^3 + y^3 + z^3 - 3xyz\) is equal to :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 38
In a skew-symmetric matrix, \(a_{ji} = -a_{ij}\):
\(y = a_{21} = -a_{12} = -2\)
\(z = a_{31} = -a_{13} = 3\)
\(x = a_{32} = -a_{23} = 1\)
Then
\(x^3 + y^3 + z^3 = 1 - 8 + 27 = 20\)
\(3xyz = 3(1)(-2)(3) = -18\)
\(x^3 + y^3 + z^3 - 3xyz = 20 - (-18) = 38\)