If [ x y z 2 u v - 1 6 w ] is a skew symmetric matrix, then the value of x 2 + y 2 + z 2 + u 2 + v 2 + w 2 is:

Question

If $[\begin{matrix} x & y & z \\ 2 & u & v \\ - 1 & 6 & w \end{matrix}]$ is a skew symmetric matrix, then the value of $x^{2} + y^{2} + z^{2} + u^{2} + v^{2} + w^{2}$ is:

Smart Achievers · Accepted Answer

(4)

Ans. 41

Explanation:

For a skew symmetric matrix,

$\Rightarrow$ $A^{'} = - A$

$\Rightarrow$ $[\begin{matrix} x & 2 & - 1 \\ y & u & 6 \\ z & v & w \end{matrix}] = [\begin{matrix} - x & - y & - z \\ - 2 & u & - v \\ 1 & - 6 & - w \end{matrix}]$

Comparing the corresponding elements,

$\Rightarrow$ $y = - 2, v = - 6, z = 1$

$x = 0, u = 0, w = 0$

$∴$ $x^{2} + y^{2} + z^{2} + u^{2} + v^{2} + w^{2} = 0 + 4 + 1 + 0 + 36 + 0 = 41$

Solution

Q.
If $[\begin{matrix} x & y & z \\ 2 & u & v \\ - 1 & 6 & w \end{matrix}]$ is a skew symmetric matrix, then the value of $x^{2} + y^{2} + z^{2} + u^{2} + v^{2} + w^{2}$ is:

1 1

2 4

3 36

4 41

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Solution

Q. If [xyz2uv-16w] is a skew symmetric matrix, then the value of x2+y2+z2+u2+v2+w2 is:

1 1

2 4

3 36

4 41

Ans. (4) Ans. 41 Explanation: For a skew symmetric matrix, ⇒ A'=-A ⇒ [x2-1yu6zvw]=[-x-y-z-2u-v1-6-w] Comparing the corresponding elements, ⇒ y=-2, v=-6, z=1 x=0, u=0, w=0 ∴ x2+y2+z2+u2+v2+w2=0+4+1+0+36+0=41

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Q.
If $[\begin{matrix} x & y & z \\ 2 & u & v \\ - 1 & 6 & w \end{matrix}]$ is a skew symmetric matrix, then the value of $x^{2} + y^{2} + z^{2} + u^{2} + v^{2} + w^{2}$ is: