Let the 2 x 2 matrix A have real, distinct eigenvalues A and μ. Suppose that an eigenvector of A is (1,0) and an eigenvector of μ is (-1,1). Sketch the phase portraits of x = Ax for the following cases: (a) 0 < λ < μ, (b) 0 <μ < λ (c)λ <μ<0 (d) λ < 0 < μ (e)μ < 0 < λ (f) λ = 0, μ > 0.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let the 2 x 2 matrix A have real, distinct eigenvalues A and μ. Suppose
that an eigenvector of X is (1,0) and an eigenvector of μ is (-1,1).
Sketch the phase portraits of x = Ax for the following cases:
(a) 0 < λ < μ, (b) 0 <μ < λ (c) λ<μ<0
(d) λ < 0 < μ (e)μ < 0 < λ (f) λ = 0, μ > 0.
Transcribed Image Text:Let the 2 x 2 matrix A have real, distinct eigenvalues A and μ. Suppose that an eigenvector of X is (1,0) and an eigenvector of μ is (-1,1). Sketch the phase portraits of x = Ax for the following cases: (a) 0 < λ < μ, (b) 0 <μ < λ (c) λ<μ<0 (d) λ < 0 < μ (e)μ < 0 < λ (f) λ = 0, μ > 0.
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