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Given a matrix $A$, size $(n-1) \times n$ over $\mathbb{R}$, whose all entries are either $1$ or $0$, my experiments show that all its solutions are formed by coordinates of $c$,$-c$ and zero (for a real constant $c$).

However, I can't find a way to prove it. Can anyone suggest a proof or construct a counter example?

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    Solutions? You solve a linear system, but not a matrix...2011-09-16
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    It is most probably because you're solving $Ax=0$ and the remaining $1\times n$ row is your solution transposed. Is that correct ?2011-09-16
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    I meant to make your A square and full rank, sorry I guess i need more coffee :)2011-09-16

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