Let $\lambda$ be an eigenvalue of $B$ and $Y = \left(\begin{array}{c} y_{1} \\ \vdots \\ y_{q} \end{array}\right)$ an associated eigenvector. Show that, if we impose $y_{0} = y_{q+1} = 0$, then, for all $k \in \llbracket 1, q \rrbracket$, $y_{k-1} - \lambda y_{k} + y_{k+1} = 0$.