Hey! I’m quite stuck on the question below. Thanks!
Let $v$ be an eigenvector of the $n \times n$ matrix $M$ corresponding to the eigenvalue $\lambda$. Set $Q = [v,a_2,a_3,\ldots,a_n]$ where ${v,a_2,a_3,\ldots,a_n}$ is a set of $n$ linearly independent vectors. Show that the first column of $Q^{-1}MQ$ is $(\lambda,0,0,\ldots,0)$