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PutnamSuperchallengeIntegrals I: Feynman's Trick

Integrals I: Feynman's Trick · Superchallenge problem

A 3×33\times3 real matrix AA has eigenvalues 1,2,31, 2, 3. Compute det⁡ ⁣(A2+I)\det\!\left(A^2 + I\right).