7. (i) Find the characteristic equation of the matrix A = and show that A satisfies the equation and evaluate A. (ii) Verify that the sum of the eigenvalues of A equals the trace of A and that (1 0 their product equals |A|, for the matrix 0 3 -1 0 1 3

7. (i) Find the characteristic equation of the matrix A = and show that A satisfies the equation and evaluate A. (ii) Verify that the sum of the eigenvalues of A equals the trace of A and that (1 0 their product equals |A|, for the matrix 0 3 -1 0 1 3

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

7. (i) Find the characteristic equation of the matrix A =
2
and show that A
satisfies the equation and evaluate A.
(ii) Verify that the sum of the eigenvalues of A equals the trace of A and that
(1 0
their product equals |A|, for the matrix 0 3
-1
0 1

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