Let A be the real 2x2 matrix
with bc greater than or equal to 0. Prove there exists a real 2x2 invertible matrix S so that S^-1 A S is either diagonal or of the form
where x is the eigenvalue of A.
The link between invertibility of matrices and eigenvalues is investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who posted the question.