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

For an eigenvalue $t\in \{\phi ,\psi \}$, the equation $A(x,y{)}^T=t(x,y{)}^T$ gives $x=ty$ and $(t+1)y=t^{2}y$. The second identity holds because $t^2=t+1$. Taking $y=1$ gives the eigenvectorsEach associated eigenspace consists of all scalar multiples of its displayed vector. A zero vector is excluded when speaking of an eigenvector.