Find x, y, z if [0-5ixy0z32-20] is a skew symmetric matrix.

Exercise 2.2 | Q 8 | Page 47

QUESTION

Find x, y, z if ${\displaystyle \left[\begin{array}{ccc}0& -5i& x\\ y& 0& z\\ \frac{3}{2}& -\sqrt{2}& 0\end{array}\right]}$ is a skew symmetric matrix.

SOLUTION

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

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

Since A is a skew-symmetric matrix,
A = A^T

∴ ${\displaystyle \left[\begin{array}{ccc}0& -5\text{i}& x\\ y& 0& z\\ \frac{3}{2}& -\sqrt{2}& 0\end{array}\right]}$

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

∴ By equality of matrices, we get

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

Concept: Algebra of Matrices

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board

Chapter 2 Matrices

Exercise 2.2 | Q 8 | Page 47