Find the eigenvalues of the matrix A=(3113)A = \begin{pmatrix} 3 & 1 \\ 1 & 3 \end{pmatrix}A=(3113).
λ=2\lambda = 2λ=2 and λ=3\lambda = 3λ=3
λ=4\lambda = 4λ=4 and λ=2\lambda = 2λ=2
λ=3\lambda = 3λ=3 (double root)
λ=5\lambda = 5λ=5 and λ=1\lambda = 1λ=1