find eigenvalues and eigenvectors for the following matrix
|a 1 0|
|1 a 1|
|0 1 a|
The Attempt at a Solution
I'm trying to find eigenvalues, in doing so I've come to a dead end at 1 + (a^3 - lambda a^2 -2a^2 lambda + 2a lambda^2 + lambda^2 a - lambda^3 - a + lambda)
This is because i have to put in a - lamnda across the board, then it gets tricky when trying to find eigenvalues with all these variables, can someone please help in this bizarre question.