= Solution
Use <orthogonality to the image of a matrix>. For $n=(1,2,1)^T$, the condition is $n^TA=0$, since $n^TAr$ must vanish for every nonzero input. Direct multiplication gives
$$
n^TA=(a,\ 2b+c+3,\ b+2c-1).
$$
Each coefficient must vanish; choosing the three coordinate <basis vectors> as inputs already proves necessity. Solve $2b+c=-3$, $b+2c=1$ to obtain
$$
\boxed{a=0,\qquad b=-\frac73,\qquad c=\frac53.}
$$
These values make every output have zero <dot product> with $n$, including any zero output. Here <orthogonality> is understood in this algebraic sense; no direction is assigned to the zero <vector>.
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