JEE Advance - Mathematics (2010 - Paper 1 Offline - No. 23)
The number of $3 \times 3$ matrices A whose entries are either 0 or 1 and for which the system
$\mathrm{A}\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has exactly two distinct solutions, is
$\mathrm{A}\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has exactly two distinct solutions, is
0
$2^9-1$
168
2
Explanation
Given,
A $\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has two distinct solution we know that three Planes cannot intersect at two distinct point.
Hence, number of $3 \times 3$ matrix $A$ is zero.
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