Consider the following $3 \times 3$ matrices.
$M_{1}=\begin{pmatrix}
0&1&1 \\
1&0&1 \\
1&1&0
\end{pmatrix} $
$M_{2}=\begin{pmatrix}
1&0&1 \\
0&0&0 \\
1&0&1
\end{pmatrix} $
How may $0-1$ column vectors of the form
$X$= $\begin{pmatrix}
x_{1} \\
x_{2} \\
x_{3}
\end{pmatrix} $
are there such that $M_{1}X = M_{2}X$ (modulo $2$)? (modulo $2$ means all operations are done modulo $2$, i.e, $3 = 1$ (modulo $2$), $4 = 0$ (modulo $2$)).
- None
- Two
- Three
- Four
- Eight