Eigenvalues and Eigenvectors

MTH-168 · Semester II · Mathematics II

Eigenvalues of a symmetric matrix

Guided practice — solve each problem, check, then generate a fresh one.

Score 0 / 0

Formula to apply

det(A − λI) = 0

Problem

Find the eigenvalues of A = [ 3 1 ] [ 1 3 ] Enter the two eigenvalues (either order).

Working

  1. 1Characteristic polynomial: λ² − (a + a)λ + (a·a − 1·1) = λ² − 6λ + 8.
  2. 2Factor: (λ − 4)(λ − 2).
  3. 3Eigenvalues: 4 and 2.