MathDB
Putnam 2015 A6

Source:

December 6, 2015
PutnamPutnam 2015Putnam matrices

Problem Statement

Let nn be a positive integer. Suppose that A,B,A,B, and MM are n×nn\times n matrices with real entries such that AM=MB,AM=MB, and such that AA and BB have the same characteristic polynomial. Prove that det⁡(A−MX)=det⁡(B−XM)\det(A-MX)=\det(B-XM) for every n×nn\times n matrix XX with real entries.
Back to ProblemsView on AoPS