The number of $3 imes 3$ matrices $A$ whose entries are either 0 or 1 and for which the system $A\left[\begin{array}{l}x \ y \ z\end{array} ight]=\left[\begin{array}{l}1 \ 0 \ 0\end{array} ight]$ has exactly two distinct solutions, is

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The number of $3 	imes 3$ matrices $A$ whose entries are either 0 or 1 and for which the system $A\left[\begin{array}{l}x \ y \ z\end{array}ight]=\left[\begin{array}{l}1 \ 0 \ 0\end{array}ight]$ has exactly two distinct solutions, is

Aicharya · Accepted Answer

Since, $A\left[\begin{array}{l}x \ y \ z\end{array}ight]=\left[\begin{array}{l}1 \ 0 \ 0\end{array}ight]$ is linear equation in three variables and that could have only unique, no solution or infinitely many solution. $	herefore$ It is not possible to have two solutions. Hence, number of matrices $A$ is zero.

The number of $3 \times 3$ matrices $A$ whose entries are either 0 or 1 and for which the system…

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