Eigenvalues of a symmetric matrix
Guided practice — solve each problem, check, then generate a fresh one.
Formula to apply
det(A − λI) = 0
Problem
Find the eigenvalues of
A = [ 4 1 ]
[ 1 4 ]
Enter the two eigenvalues (either order).
Working
- 1Characteristic polynomial: λ² − (a + a)λ + (a·a − 1·1) = λ² − 8λ + 15.
- 2Factor: (λ − 5)(λ − 3).
- 3Eigenvalues: 5 and 3.