Matrices And Determinants Ques 93
The number of $3 \times 3$ matrices $A$ whose entries are either $0$ or $1$ and for which the system $A$$ \begin{bmatrix} x \\ y \\ z \end{bmatrix} $ =$ \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} $ has exactly two distinct solutions, is
(2010)
(a) $0$
(b) $2^{9}-1$
(c) $168$
(d) $2$
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Answer:
Correct Answer: 93.(a)
Solution:
Formula:
Solution to a System of Equations:
- Since, $A$$ \begin{bmatrix} x \\ y \\ z \end{bmatrix} $ =$ \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} $ is linear equation in three variables and that could have only unique, no solution or infinitely many solution.
$\therefore$ It is not possible to have two solutions.
Hence, number of matrices $A$ is zero.
BETA
