Question

If A = $\left[\begin{array}{ccc}0&2&1\\-2&0&-2\\-1&x&0\end{array}\right]$ is a skew symmetric matrix, then find x.

Answer 1

Answer:

if A is a skew symmetric matrix than x=2

Step-by-step explanation:

$A = \left[\begin{array}{ccc}0&2&1\\-2&0&-2\\-1&x&0\end{array}\right]$

if A is a skew symmetric matrix than

$A=-A^{T} \\\\\\ \left[\begin{array}{ccc}0&2&1\\-2&0&-2\\-1&x&0\end{array}\right] =- \left[\begin{array}{ccc}0&-2&-1\\2&0&x\\1&-2&0\end{array}\right]\\\\\\\left[\begin{array}{ccc}0&2&1\\-2&0&-2\\-1&x&0\end{array}\right] =\left[\begin{array}{ccc}0&2&1\\-2&0&-x\\-1&2&0\end{array}\right]\\\\\\so\:\:x=2\\\\-x=-2\\\\x=2$