Suppose that a 4 × 4 matrix A has eigenvalues λ1 = 1, λ2 = − 4, λ3 = 6, and λ4 = − 6. Use the following method to find det (A). If p(λ) = det (λI − A) = λn + c1λn − 1 + ⋯ + cn So, on setting λ = 0, we obtain that det (− A) = cn or det (A) = (− 1)ncn Suppose that a 4× 4 matrix A has eigenvalues A1 = 1,12 = - 4, A3 = 6, and A4 = - 6. Use the following method to find det (A).Ifp(1) = det (AI - A) = A" + c1A^ -1+ ...+ CnSo, on setting A = 0, we obtain thatdet (- A) = Cn or det (A) = (- 1)^cndet (A) = i

Suppose that a 4 x 4 matrix A has eigenvalues A1 - 1, 12 - - 4, 13 = 6, and A4 = - 6. Use the following method to find det (A) If p(1) = det (AI – A) - A" + c1^ - 1 + ... + Cn So, on setting A - 0, we obtain that det (- A) = c, or det (A) = (- 1)^cn %3D det (A)

Suppose that a 4 x 4 matrix A has eigenvalues A1 - 1, 12 - - 4, 13 = 6, and A4 = - 6. Use the following method to find det (A) If p(1) = det (AI – A) - A" + c1^ - 1 + ... + Cn So, on setting A - 0, we obtain that det (- A) = c, or det (A) = (- 1)^cn %3D det (A)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter10: Matrices

Section10.5: Eigenvalues And Eigenvectors

Problem 11E

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Suppose that a 4 × 4 matrix A has eigenvalues λ1 = 1, λ2 = − 4, λ3 = 6, and λ4 = − 6. Use the following method to find det (A). If p(λ) = det (λI − A) = λn + c1λn − 1 + ⋯ + cn So, on setting λ = 0, we obtain that det (− A) = cn or det (A) = (− 1)ncn