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Study Stuff for MCA Examinations - NIMCET
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Previous Year Question (PYQs)
If $A=\begin{bmatrix}x & y & z \\ 2 & u & v \\ -1 & 6 & w\end{bmatrix}$ is skew symmetric matrix, then value of $x^2+y^2+z^2+u^2+v^2+w^2$ is:
Solution
For skew symmetric matrix,
$A^T=-A$
So diagonal elements must be zero:
$x=0,; u=0,; w=0$
Now compare off-diagonal elements:
From $(1,2)$ and $(2,1)$:
$y=-2$
From $(1,3)$ and $(3,1)$:
$z=1$
From $(2,3)$ and $(3,2)$:
$v=-6$
Now compute:
$x^2+y^2+z^2+u^2+v^2+w^2$
$=0^2+(-2)^2+1^2+0^2+(-6)^2+0^2$
$=4+1+36$
$=41$
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