Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2015 / Paper 2 / 4

The characteristic polynomial is $(1-\lambda {)}^2-4=(\lambda -3)(\lambda +1)$. For $\lambda =3$ the components are equal; for $\lambda =-1$ they are opposite. After normalization, the eigenvalues and associated eigenvectors areAn overall sign change of either normalized eigenvector is equivalent.