Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Digital systems, linear algebra, introduction to formal proof (resit) / 6 / e / Solution

A particular solution is $x_p=(1,0,-1,0{)}^T$, as direct substitution into all five equations verifies. Add any vector in the null space to obtain every solution:Conversely, the difference of any two solutions is annihilated by $A$, so there are no further solutions. This is the affine solution space of a consistent linear system.