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Suppose that a 4 x 4 matrix A has eigenvalues A₁ = 1,1₂ = -4,13 = 7, and A4 = - 7. Use the following method to find tr(A).

Suppose that a 4 x 4 matrix A has eigenvalues A₁ = 1,1₂ = -4,13 = 7, and A4 = - 7. Use the following method to find tr(A).

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 80E
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Suppose that a 4 x 4 matrix A has eigenvalues A₁ = 1, A2=-4, A3 = 7, and A4 = - 7. Use the following method to find tr(A). If A is a square matrix and p(A) = det (Al-A) is the characteristic polynomial of A, then the coefficient of An-1 in p() is the negative of the trace of A. tr(A) = i
Transcribed Image Text:Suppose that a 4 x 4 matrix A has eigenvalues A₁ = 1, A2=-4, A3 = 7, and A4 = - 7. Use the following method to find tr(A). If A is a square matrix and p(A) = det (Al-A) is the characteristic polynomial of A, then the coefficient of An-1 in p() is the negative of the trace of A. tr(A) = i
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