Number of 3 × 3 matrices A whose entries are either 0 or 1 and for which system mathrm{A}left

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14.Probability

hard

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

A

$0$

B

$2^9-1$

C

$168$

D

$2$

(IIT-2010)

Solution

Three planes cannot intersect at two distinct points.

Standard 11

Mathematics

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