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Let D E L(V, V ) and let v E V be such that for some k E { 1, 2, ...}, Dku # 0 but Dk+lu = 0. 1. Show that U = Span(v, D(v), D2 (v), D*(v)) is an invariant subspace for the operator D. 2. By the result of Part 1, we may view D as an element of L(U, U). Find a basis for U which puts D into Jordan Canonical Form, and justify your result