Answer to Question #293093 in Linear Algebra for jmmm

Question

Suppose that a 4 × 4 matrix A has eigenvalues λ₁ = 1, λ₂ = − 5, λ₃ = 6, and λ₄ = − 6. Use the following method to find tr(A).

If A is a square matrix and p(λ) = det (λI − A) is the characteristic polynomial of A, then the coefficient of λ^{n − 1} in p(λ) is the negative of the trace of A.