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Suppose that a 4 x 4 matrix A has eigenvalues A₁ = 1, A₂=-5, A3 = 7, and A4 = -7. Use the following method to find det (A). If So, on setting A = 0, we obtain that det (A) = i Sa.e p(A) = det (Al-A) = A + C₁-1+...+ Cn det (-A) = Cn or det (A) = (-1)^cn

Suppose that a 4 x 4 matrix A has eigenvalues A₁ = 1, A₂=-5, A3 = 7, and A4 = -7. Use the following method to find det (A). If So, on setting A = 0, we obtain that det (A) = i Sa.e p(A) = det (Al-A) = A + C₁-1+...+ Cn det (-A) = Cn or det (A) = (-1)^cn

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=-5, A3 = 7, and A4 = - 7. Use the following method to find det (A). If So, on setting λ = 0, we obtain that det (A) = i Sa.e p(A) = det (Al-A) = A +₁¹+...+₁ det (-A) = C₁ or det (A) = (-1)^cn
Transcribed Image Text:Suppose that a 4 x 4 matrix A has eigenvalues A₁ = 1, A₂=-5, A3 = 7, and A4 = - 7. Use the following method to find det (A). If So, on setting λ = 0, we obtain that det (A) = i Sa.e p(A) = det (Al-A) = A +₁¹+...+₁ det (-A) = C₁ or det (A) = (-1)^cn
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