Matrix A Satisfies A²⁰+αA¹⁹+βA=Given Matrix — Find β−α
Given a triangular matrix A satisfying A²⁰+αA¹⁹+βA equals a specific matrix, find β−α using the eigenvalues on A’s diagonal.
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Sum of Prime Factors of |P⁻¹AP−2I| for Given 3×3 Matrices A, P
Given 3×3 matrices A and P, find the sum of the prime factors of |P⁻¹AP−2I| using the property that similar matrices share the same determinant after shifting by 2I.