Answer the question as a discussion with a minimum of 30 words: If A is a an n x n matrix then det(A – sI) is an nth degree polynomial. The zeros of this polynomial are the eigenvalues for the system....

Answer the question as a discussion with a minimum of 30 words: If A is a an n x n matrix then det(A – sI) is an nth degree polynomial. The zeros of this polynomial are the eigenvalues for the system. So, to find the eigenvalues for a system means solving a polynomial equation. This is generally not too computationally difficult if n is kept small, but nothing says we have to keep n small. For this prompt, first discuss all types of eigenvalues possible. That is, suppose s1, s2, s3, …, sn is the complete list of solutions to the characteristic polynomial det(A – sI) = 0. (Note: the list includes all zeros of the polynomial, counting their repetition, if necessary.) Then answer: Is it possible for a system of linear first order differential equation to not have associated eigenvalues? Why or why not?