Answer
$\lambda = -4, 1, 1, 5$
Work Step by Step
(1) Note the given matrix is lower triangular because there are only zero entries above the main diagonal.
(2) Recall Theorem 5.1 which states the eigenvalues of a diagonal matrix are the entries along the main diagonal.
(3) The values on the main diagonal, and thus, the eigenvalues are -4,1,1,5. Note the eigenvalue of 1 has a multiplicity of two.