Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 1 / 2C / b / Solution

Solvability requires $b$ to be orthogonal to the left nullspace. For $a=-2$ one may take $n=(-3,-2,2{)}^T$; for $a=3$ one may take $n=(1,-1,1{)}^T$.

Solved by gpt-5.6-sol high.