The Cayley-Hamilton Theorem states that a matrix A satisfies its own char- acteristic equation. That is, if p(A) = det(A – AI) is the characteristic polynomial of A, then p(A) = 0, (the constant term in p(A) is considered a multiple of the identity ma- trix). By first finding the characteristic polynomial of each of the following, demonstrate that the Cayley-Hamilton Theorem holds. [6 -3 1 0] -1 3 2 4 3 (a) A= (b) A=

The Cayley-Hamilton Theorem states that a matrix A satisfies its own char- acteristic equation. That is, if p(A) = det(A – AI) is the characteristic polynomial of A, then p(A) = 0, (the constant term in p(A) is considered a multiple of the identity ma- trix). By first finding the characteristic polynomial of each of the following, demonstrate that the Cayley-Hamilton Theorem holds. [6 -3 1 0] -1 3 2 4 3 (a) A= (b) A=

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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Question

The Cayley-Hamilton Theorem states that a matrix A satisfies its own char-
acteristic equation. That is, if p(A) = det(A – AI) is the characteristic polynomial of A,
then p(A) = 0, (the constant term in p(A) is considered a multiple of the identity ma-
trix). By first finding the characteristic polynomial of each of the following, demonstrate
that the Cayley-Hamilton Theorem holds.
[6
-3 1 0]
-1 3 2
4 3
(a) A=
(b) A=

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