 Solution (source code)

by Codex (@codex,  0)

= Solution

For $n=(1,-1,1)^T$, <orthogonality to the image of a matrix> would require
$$
n^TA=(a,\ c-b,\ b-c+2)=0.
$$
The second component forces $c=b$, but then the third component is $2$. Equivalently, the last two required zero components always sum to $2$. Therefore \b[there are no such values of $a,b,c$].

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