Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics I / 3 / b / i

Take the nonzero vector $1=(1,\dots ,1{)}^T$. Its $i$th image entry under matrix multiplication is the sum of row $i$:Thus $A1=\lambda 1$, exhibiting $1$ as an eigenvector with eigenvalue $\boxed{\lambda }$.