EXERCISE T2.3(a) Verify equation (2.20). (b) Use equation (2.21) to show that the fixedpoint (0, 0) is a sink if |a| < 1 and a source if |a| > I. The eigenvalues of an upper triangular matrix are its diagonal entries, so thematrix has a repeated eigenvalue of a. Check thatAn = an-n-1Therefore the effect of A" on vectors isa(32)aax nyAn1² (²) = 21²-1 (1²x+1²)an-1ay(2.20)(2.21)

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Answered: The eigenvalues of an upper triangular…

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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The eigenvalues of an upper triangular matrix are its diagonal entries, so the matrix has a repeated eigenvalue of a. Check that - (2) Anan-1 = Therefore the effect of A" on vectors is ax ny A^ (3) - 2²-1₁ ( x + 1) =an-1 = ay (2.20) (2.21)