) Let T' be a linear operator on a vector space V and let W be a T-invariant subspace of V. Let n : V →V\W be the usual quotient map sending n(v) = v+W for v EV. Prove that T descends to a linear map on the quotient V\W that commutes with n. That is, show that the map T : V\W →V\W_defined by T(v+W):= T(v)+W is a well-defined linear operator on V \ W that satisfies ŋT = Tŋ.

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