Questions

The number of $3\times 3$ matrices $A$ whose entries are either $0\text{\hspace{0.17em}}\text{\hspace{0.17em}}or\text{\hspace{0.17em}}\text{\hspace{0.17em}}1$ and for which the system $A\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]$ has exactly two distinct solutions, is

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a

0

b

29−1

c

168

d

2

detailed solution

Correct option is A

Since, Axyz=100 is linear equation in three variables and that could have only unique, no solution or infinitely many solutions.∴ It is the possible to have two solutionsHence, number of matrices A is zero.

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