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Question

Let T be a linear operator on a finite-dimensional vector space V. Suppose that V is a direct sum of T-invariant subspaces, say V = W_{1} ꚛ W_{2} ꚛ ...ꚛ W_{k}. Prove that det(T) = det(T_{w1}).det(T_{w2}).....det(T_{wk}).

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