Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Digital systems, linear algebra, introduction to formal proof / 4 / a / Solution

No: the only solution is the zero vector. Subtract the fourth row equation from the first to get $2x_3=0$. Subtract the third from the fourth to get $2x_2=0$. With $x_2=x_3=0$, any row then gives $x_1=0$. Thus this homogeneous linear system has trivial null space.