Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Digital systems, linear algebra, introduction to formal proof / 1 / b / Solution

For a square matrix $M$, an eigenvalue–eigenvector pair consists of a scalar $\lambda$ and a nonzero vector $v$ satisfyingThe linear map represented by $M$ therefore scales $v$ by $\lambda$. The exclusion of the zero vector matters: otherwise every scalar would satisfy the equation trivially.