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For the following matrices A, Computo AT. If A is a 2x2 matrix with real, different eigenvalues, draw the phase portraits. a) A = (-108/₂2 -=-1-2/ ·1.8 -0.8

For the following matrices A, Computo AT. If A is a 2x2 matrix with real, different eigenvalues, draw the phase portraits. a) A = (-108/₂2 -=-1-2/ ·1.8 -0.8

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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For the following matrices A, Computo AT. If A is a 2x2 matrix with real, different eigenvalues, draw the phase portraits. a) A₂= /-1.8 -0.8° a) A= ( -1.2 -0.2
Transcribed Image Text:For the following matrices A, Computo AT. If A is a 2x2 matrix with real, different eigenvalues, draw the phase portraits. a) A₂= /-1.8 -0.8° a) A= ( -1.2 -0.2
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Now, e At 2₁ = -19 The coresponding eigen vectors are, +1 (1) 22- ₂² (1) Hence, the matrix exponential should be: et 1) (( ²² e+)( et (1 Cette 。 6 22 the L e-t et - 16e-t -et-ge-t. 2 5/ (C) (1 4 - e² + 4e-t et tet -1 Since the eigen values are 1₁= -1 and 1₂ = -2 shouldn't e At = VOV¹ v@v- 3 (= + (-26) ?
Transcribed Image Text:Now, e At 2₁ = -19 The coresponding eigen vectors are, +1 (1) 22- ₂² (1) Hence, the matrix exponential should be: et 1) (( ²² e+)( et (1 Cette 。 6 22 the L e-t et - 16e-t -et-ge-t. 2 5/ (C) (1 4 - e² + 4e-t et tet -1 Since the eigen values are 1₁= -1 and 1₂ = -2 shouldn't e At = VOV¹ v@v- 3 (= + (-26) ?
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