Let $\mathscr{A}$ be the set of all $3 \times 3$ symmetric matrices all of whose entries are either 0 or 1 . Five of these entries are 1 and four of them are 0 .

The number of matrices $A$ in $\mathscr{A}$ for which the system of linear equations $A\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ is inconsistent, is