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 / b / Solution

Denote the five rows by $r_1,\dots ,r_5$. They satisfyThus $r_2,r_3,r_4$ span the row space. They are linearly independent: in a linear combination $\alpha r_2+\beta r_3+\gamma r_4=0$, coordinate 1 gives $\alpha =0$, coordinate 2 then gives $\beta =0$, and coordinate 4 gives $\gamma =0$. ThereforeAs an alternative basis, the nonzero rows of the reduced row echelon form are