Algebra 2 Honors Practice Test

The eigenvalues come from solving det(A − λI) = 0. For the matrix A = [[2, 1], [1, 2]], compute det[[2−λ, 1], [1, 2−λ]] = (2−λ)(2−λ) − 1 = (2−λ)^2 − 1 = λ^2 − 4λ + 3. Factor this as (λ − 1)(λ − 3) = 0, giving λ = 1 or λ = 3. So the eigenvalues are 1 and 3. (Being symmetric, the matrix has real eigenvalues, which matches these results.)