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(1) Show that b3 = 1, b2 = -Tr(A) i.e. the trace of A, and bo = -det(A). (2) Give an example of C = diag(cı, c2, c3) and D = diag(dı, d2, d3) where Tr(C) = Tr(D), det(C

(1) Show that b3 = 1, b2 = -Tr(A) i.e. the trace of A, and bo = -det(A). (2) Give an example of C = diag(cı, c2, c3) and D = diag(dı, d2, d3) where Tr(C) = Tr(D), det(C

Advanced Engineering Mathematics
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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a1 a2 diag(a1, a2, ... , An) An Question 1 b3x3 + b2x2 + b1x + bo. Suppose that A = diag(a1, a2, a3) and suppose that the characteristic polynomial CA(x) = (1) Show that b3 = 1, b2 = -Tr(A) i.e. the trace of A, and bo = -det(A). (2) Give an example of C = diag(cı, c2, c3) and D = diag(dı, d2, d3) where Tr(C) = Tr(D), det(C) = det (D), but C is not similar to D.
Transcribed Image Text:a1 a2 diag(a1, a2, ... , An) An Question 1 b3x3 + b2x2 + b1x + bo. Suppose that A = diag(a1, a2, a3) and suppose that the characteristic polynomial CA(x) = (1) Show that b3 = 1, b2 = -Tr(A) i.e. the trace of A, and bo = -det(A). (2) Give an example of C = diag(cı, c2, c3) and D = diag(dı, d2, d3) where Tr(C) = Tr(D), det(C) = det (D), but C is not similar to D.
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