Chapter 2 - Matrices and Systems of Linear Equations - 2.1 Matrices: Definitions and Notation - Problems - Page 122: 23

$\begin{bmatrix} 0 & 3 & -1 & -1\\ -3 & 0 & -7 & 9\\ 1 & 7 & 0 & -2 \\ 1 & 9 & 2 & 0 \\ \end{bmatrix}$

Make $a_{ij}=-a_{ji}$, if $i\ne j$ If $j=i$, $a_{ii}=-a_{ii}$. So, $a_{ii}=0$. That is, the elements of the main diagonal must be equal to zero. Example: $\begin{bmatrix} 0 & 3 & -1 & -1\\ -3 & 0 & -7 & 9\\ 1 & 7 & 0 & -2 \\ 1 & 9 & 2 & 0 \\ \end{bmatrix}$