Question #1379

(a) Let A be a square matrix and fA(x) (x = lambda) its characteristic polynomial. In each of the following cases (i) to (iv), write down whether
(D) A is diagonalizable over R
(N) A is not diagonalizable over R
(U) it is not possible to say one way or the other.
(i) fA(x) = (x - 3)^2(x - 5)
(ii) fA(x) = (x^2 - 1)(x^2 - 2)
(iii) fA(x) = (x^2 + 6)(x - 1)(X + 2)
(iv) fA(x) = (x^2 + 3)^2
(b) For each case that you marked (N), say whether or not the matrix can
certainly be diagonalized over C

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