Hello,

I need some help with this problem:

$\displaystyle \begin{pmatrix} 1 & 0 & 1 & 0 & \cdots \\ 0 & 1 & 0 & 1 & \cdots \\ 1 & 0 & 1 & 0 & \cdots \\ 0 & 1 & 0 & 1 & \cdots \\ \vdots & \vdots & \vdots & \vdots & \ddots \end{pmatrix}$

The instructions are to find the eigenvalues and eigenvectors of this n by n matrix. I've tried to use $\displaystyle det(A -\lambda I_n) = 0$ to get the characteristic polynomial, but I can't seem to finish it.

I'd be grateful for any hints.