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Answer to Question #1379 in Linear Algebra for AA

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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