Given a matrix A = a b and denoting its eigenvalues by 2₁ and 22 (note that these can be the same value), prove that det(A) = 2₁λ2 and Tr(A) = λ₁ + λ2, where Tr(A) = a + d.

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 15E
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Given a matrix A =
a
b
and denoting its eigenvalues by 2₁ and 22 (note that these can be the
same value), prove that det(A) = 2₁λ2 and Tr(A) = λ₁ + λ2, where Tr(A) = a + d.
Transcribed Image Text:Given a matrix A = a b and denoting its eigenvalues by 2₁ and 22 (note that these can be the same value), prove that det(A) = 2₁λ2 and Tr(A) = λ₁ + λ2, where Tr(A) = a + d.
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