 Solution

ID: 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 is

H = 2 v v^{T} - I = \frac{1}{25} (- 7 24 247) .

Indeed

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.

 New to topics? Read the docs here!