Problem 3. Consider the matrices 2 0 0 0 0 1 3 -1 3 -1 A = В 0 -1 0 0 -1 3 3 0 0 2 (a) Show that A and B have the same eigenvalues, but have different eigenspaces. (b) Find invertible matrices P and Q and a diagonal matrix A such that A and B factor as A = PAP¯' and B = QAQ-', or explain why this is not possible.

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