The characteristic equation of the coefficient matrix A of the system

is

Therefore, A has the repeated complex conjugate pair 3 ± 4i of eigenvalues. First show that the complex vectors

form a length 2 chain {v₁, v₂} associated with the eigenvalue λ = 3 - 4i . Then calculate the real and imaginary parts of the complex-valued solutions

to find four independent real-valued solutions of x' = Ax.

Transcribed Image Text:

X' 3-4 4 0 0 1 3 0 0 0 34 0 1 -4 3 X