Question: 3. Define M = 0 0 0 0 3 -1 0-1 3 (a) Name an easily observable property of the matrix M that guarantees

3. Define M = 0 0 0 0 3 -1 0-1 3 (a) Name an easily observable property of the matrix M that guarantees that it is diagonalizable. (b) Compute the characteristic polynomial PM(A) of M and find all its zeros. (c) Find a basis of R3 consisting of eigenvectors of M. (d) Find a 3 x 3 invertible matrix P and a 3 x 3 diagonal matrix D such that M PDP-. =

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