Number of 3 × 3 matrices A , whose entries are either 1 or -1 and for which the system&nb

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3 and 4 .Determinants and Matrices

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The number of $3 \times 3$ matrices $A$, whose entries are either $1$ or $-1$ and for which the system $A\left[ {\begin{array}{{20}{c}}
x\\
y\\
z
\end{array}} \right] = \left[ {\begin{array}{{20}{c}}
1\\
{ - 1}\\
0
\end{array}} \right]$ has exactly three distinct solutions, is

A

$0$

B

$2^9 - 1$

C

$168$

D

$2$

Solution

It is not possible that three planes intersect exactly at $3$ points . So no such matrix possible

Standard 12

Mathematics

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