 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/c/solution

det (t I - A) = det (t - 1 - 1 - 1 t) = t^{2} - t - 1.

Its two distinct real roots are the eigenvalues

φ = \frac{1 + 5}{2} > 0, ψ = \frac{1 - 5}{2} < 0.

Their product is

- 1

, so

ψ = - 1/ φ

. Equivalently,

φ^{2} = φ + 1

implies

1/ φ = φ - 1

. The positive eigenvalue is the golden ratio.

 New to topics? Read the docs here!