Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Digital systems, linear algebra, introduction to formal proof / 4 / c / ii / Solution

Apply the same permutation to the right-hand side and solve two triangular systems. Forward substitution in $Ly=Pb$ givesso $y=(3,-6,-11{)}^T$. Back substitution in $Ux=y$ gives $-11x_3=-11$, $4x_2-2x_3=-6$, and $3x_1+x_2+4x_3=3$. Therefore $x=(0,-1,1{)}^T$. Substitution in the original system returns $(3,-2,0{)}^T$, as required.