 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/digital-systems-linear-algebra-introduction-to-formal-proof-resit/4/d/solution

t \in {φ, ψ}

A (x, y)^{T} = t (x, y)^{T}

gives

x = t y

and

(t + 1) y = t^{2} y

. The second identity holds because

t^{2} = t + 1

. Taking

y = 1

v_{φ} = (φ 1), v_{ψ} = (ψ 1) .

Each associated eigenspace consists of all scalar multiples of its displayed vector. A zero vector is excluded when speaking of an eigenvector.

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