Matrices and Determinants 4 Question 17
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18. The number of $3 \times 3$ matrices $A$ whose entries are either $x \quad 1$ 0 or 1 and for which the system $A y=0$ has exactly z 0
======= ####18. The number of $3 \times 3$ matrices $A$ whose entries are either $0$ or $1$ and for which the system $A$$ \begin{bmatrix} x \\ y \\ z \end{bmatrix} $ =$ \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} $ has exactly
3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed two distinct solutions, is
(2010)
(a) 0
(b) $2^{9}-1$
(c) 168
(d) 2
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Answer:
Correct Answer: 18. (a)
Solution:
- Since, $A$$ \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.
