The sum of the diagonal entries (the trace) equals the sum of the eigenvalues: A = [~ ~]

Chapter 6, Problem 17

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The sum of the diagonal entries (the trace) equals the sum of the eigenvalues: A = [~ ~] has det(A - A/) = A 2 - (a + d)A + ad - bc = O. The quadratic formula gives the eigenvalues A = (a +d + r)/2 and A = __ Their sum is . If A has Al = 3 and A2 = 4 then det(A - AI) = _

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