MathDB
Romanian District Olympiad

Source: Grade XI

March 17, 2010
linear algebramatrixalgebrapolynomialfunctionlinear algebra unsolved

Problem Statement

Consider the matrix A,B∈lM3(C) A,B\in \mathcal l{M}_3(\mathbb{C}) with A=−tA A=-^tA and B=tB B=^tB. Prove that if the polinomial function defined by f(x)=det⁡(A+xB) f(x)=\det(A+xB) has a multiple root, then det⁡(A+B)=det⁡B \det(A+B)=\det B.
Back to ProblemsView on AoPS