Exercises 23 and 24 show how to classify a quadratic form Q(x) = xTAx, when
23. If λ1 and λ2 are the eigenvalues of A, then the characteristic polynomial of A can be written in two ways: det(A − λI) and (λ − λ1)(λ − λ2). Use this fact to show that λ1 + λ2 = a + d (the diagonal entries of A) and λ1λ2 = det A.
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