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Problem
Problem
The number of
3
×
3
3 \times 3
3
×
3
matrices
A
A
A
whose entries are either
0
0
0
or
1
1
1
and for which the system
A
[
x
y
z
]
=
[
1
1
0
]
A \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix}
A
x
y
z
=
1
1
0
has exactly two distinct solutions, is a. 0 b.
2
9
−
1
2^9 - 1
2
9
−
1
c. 168 d. 2
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