Determinants and Matrices — Maths STD 11 Science — Question

$\therefore \quad A^{\mathrm{T}}=\left[\begin{array}{ccc}0 & y & \frac{3}{2} \\ -5 i & 0 & -\sqrt{2} \\ x & z & 0\end{array}\right]$

Since $\mathrm{A}$ is a skew-symmetric matrix,

$\mathrm{A}=-\mathrm{A}^{\mathrm{T}}$

$\therefore \quad\left[\begin{array}{ccc}0 & -5 i & x \\ y & 0 & \mathrm{z} \\ \frac{3}{2} & -\sqrt{2} & 0\end{array}\right]=-\left[\begin{array}{ccc}0 & y & \frac{3}{2} \\ -5 i & 0 & -\sqrt{2} \\ x & z & 0\end{array}\right]$

$\therefore \quad\left[\begin{array}{ccc}0 & -5 \mathrm{i} & x \\ y & 0 & z \\ \frac{3}{2} & -\sqrt{2} & 0\end{array}\right]=\left[\begin{array}{ccc}0 & -y & \frac{-3}{2} \\ 5 \mathrm{i} & 0 & \sqrt{2} \\ -x & -z & 0\end{array}\right]$

$\therefore \quad$ By equality of matrices, we get

$x=\frac{-3}{2}, y=5 i, z=\sqrt{2}$