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 $$A \left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right]$$ has a unique solution, is (A) less than 4 (B) at least 4 but less than 7 (C) at least 7 but less than 10 (D) at least 10
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
$$A \left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right]$$
has a unique solution, is\\
(A) less than 4\\
(B) at least 4 but less than 7\\
(C) at least 7 but less than 10\\
(D) at least 10