Question: Please help me solve these! 1. [5] Call a matrix M orthogonally diogonahzoble if there is an orthogonal matrix P such that P'IM P is

Please help me solve these!

1. [5] Call a matrix M orthogonally diogonahzoble if there is an orthogonal matrix P such that P'IM P is diagonal. Prove that every orthogonally diagonalizable matrix is symmetric. 2. [5] Write all similarity types of 5 x 5 matrices M such that 3 is the only eigenvalue of M, and give the minimal polynomial of each. (Hint: There are 7 types. Use Jordan blocks to construct your matrices.)

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