Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Digital systems, linear algebra, introduction to formal proof / 6 / b / i / Solution

A unit vector along the line is $v=(3,4{)}^T/5$. Reflection fixes its component parallel to $v$ and negates its perpendicular component, so the reflection matrix isIndeed $H(3,4{)}^T=(3,4{)}^T$, $H(-4,3{)}^T=-(-4,3{)}^T$ and $H^2=I$. These characterize the orthogonal reflection in that line.