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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)

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)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 34E
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EXERCISE T2.3 (a) Verify equation (2.20). (b) Use equation (2.21) to show that the fixed point (0, 0) is a sink if |a| < 1 and a source if |a| > I.
Transcribed Image Text:EXERCISE T2.3 (a) Verify equation (2.20). (b) Use equation (2.21) to show that the fixed point (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 the matrix has a repeated eigenvalue of a. Check that An = an- n-1 Therefore the effect of A" on vectors is a (32) a ax ny An 1² (²) = 21²-1 (1²x+1²) an-1 ay (2.20) (2.21)
Transcribed Image Text:The eigenvalues of an upper triangular matrix are its diagonal entries, so the matrix has a repeated eigenvalue of a. Check that An = an- n-1 Therefore the effect of A" on vectors is a (32) a ax ny An 1² (²) = 21²-1 (1²x+1²) an-1 ay (2.20) (2.21)
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