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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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