Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Digital systems, linear algebra, introduction to formal proof (resit) / 6 / d

The reduced row echelon form gives $x_1+x_4=0$, $x_2-x_4=0$, and $x_3+x_4=0$. With free parameter $x_4=t$,The displayed nonzero vector therefore forms a basis for the null space:This agrees with the rank-nullity theorem: there are four columns and matrix rank three.