Is there any fast way to compute the determinant of this matrix:
$ \begin{vmatrix} a & b & 0 &0 &0 \\ b & a & b &0 &0 \\ 0 & b & a &b &0 \\ 0 & 0 & b &a &b \\ 0 & 0 & 0 &b &a \end{vmatrix} $
And can you say anything about $ \frac{det(M_{k+1})}{det(M_{k})} $
where $M_{k}$ is a toeplitz matrix?