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 / 6 / a / i / Solution

For $u=(1,1,1{)}^T$, the all-ones matrix is $A=u{u}^T$, so $Au=3u$ and $Av=0$ whenever $v_1+v_2+v_3=0$. These subspaces have dimensions one and two and span ${\mathbb{R}}^3$. Thus the eigenvalues are $3$ and $0$.