Question

Consider the following system. (A computer algebra system is recommended.) dx = -5 0x dt * 0 -5)^ (a) Find the eigenvalues and eigenvectors. (Order eigenvalues from smallest to largest real part, then by imaginary part. For repeated eigenvalues, list the eigenvalue once and give a maximal set of linearly independent eigenvectors.) 3, has eigenvector(s)

I'm completely stumped on these. I don't know how to proceed once I get to the eigenvalue since my typical method for solving would be to set Ax=$\lambda$x , then solve. However, this would give me -5x₁=-5x₁ and -5x₂=-5x₂ which makes A trivial. I just realized that means the eigenvectors will be <1,0> and <0,1>, but I'm still stumped on parts b and c.

Answer 1

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