Answer to Question #340870 in Linear Algebra for Dusty

Question

find the values for x, y, and z such the matrix below is skew symmetric.

0 x 3

2 y -1

z 1 0

Answer 1

$$A=\begin{pmatrix} 0 & x & 3\\ 2 & y & -1 \\ z & 1 & 0 \\ \end{pmatrix}$$

Given matrix is skew symmetric matrix:

$$A'=-A$$

$$\begin{pmatrix} 0 & 2 & z\\ x & y & 1 \\ 3 & -1 & 0 \\ \end{pmatrix}=\begin{pmatrix} 0 & -x & -3\\ -2 & -y & 1 \\ -z & -1 & 0 \\ \end{pmatrix}$$

On comparing we get:

$$x=-2, y=0, z=-3$$