Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / 11 / d

For $n=(1,-1,1{)}^T$, orthogonality to the image of a matrix would requireThe second component forces $c=b$, but then the third component is $2$. Equivalently, the last two required zero components always sum to $2$. Therefore there are no such values of $a,b,c$.