Q1)

Explain why 2 x 2 rotation matrices cannot be diagonalized (using real matrices). Your answer should demonstrate an understanding of the concepts involved in diagonalization, and should include the definitions of eigenvalues and vectors.

Q2)

Suppose that A is a 3 x 3 matrix for the reflection across the plane 2x + 3y - 5z = 0. What are the eigenvalues of A? Explain your answer. This problem can be done without any computations, just think about the definition of eigenvalues and eigenvectors, and then imagine what happens in a reflection.