I was expecting eigenvalues 0, 1, 3 (that's what I got with WolframAlpha and SageMath). What happened?
julia> using LinearAlgebra
julia> eigvals([1 -1 0; -1 2 -1; 0 -1 1])
3-element Array{Float64,1}:
3.9250536344271737e-17
0.9999999999999998
3.0