Aspire Faculty ID #17256 · Topic: CUET UG 2022 Applied Mathematics · Just now
CUET UG 2022 Applied Mathematics

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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