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1. Let, A ERX. Show that the following statements are equivalent, a) A is cyclic b) there exists an invertible matrix P such that P-1

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1. Let, A ER"X. Show that the following statements are equivalent, a) A is cyclic b) there exists an invertible matrix P such that P-1 AP has a companion form c) for all 1, rank (XI A) > n-1

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