Let T be linear operator on a finite-dimensional vector space V, and let Wi and W2 be

Chapter 7, Problem 14

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Let T be linear operator on a finite-dimensional vector space V, and let Wi and W2 be T-invariant subspaces of V such that V = W| W2. Suppose that pi(t) and p2(t) are the minimal polynomials of Tw, and Tw2, respectively. Prove or disprove; that p\{t)p2(t) is the minimal polynomial of T

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