Consider the matrix recurrence (anan−1)=M(an−1an−2)\begin{pmatrix} a_n \\ a_{n-1} \end{pmatrix} = M \begin{pmatrix} a_{n-1} \\ a_{n-2} \end{pmatrix}(anan−1)=M(an−1an−2) where M=(3110)M = \begin{pmatrix} 3 & 1 \\ 1 & 0 \end{pmatrix}M=(3110). What are the eigenvalues of MMM?
λ1=3+132,λ2=3−132\lambda_1 = \frac{3+\sqrt{13}}{2}, \lambda_2 = \frac{3-\sqrt{13}}{2}λ1=23+13,λ2=23−13
λ1=3,λ2=1\lambda_1 = 3, \lambda_2 = 1λ1=3,λ2=1
λ1=2,λ2=1\lambda_1 = 2, \lambda_2 = 1λ1=2,λ2=1
λ1=4,λ2=−1\lambda_1 = 4, \lambda_2 = -1λ1=4,λ2=−1