Answer to Question #95866 in Linear Algebra for Ananna Mitra

Question

Let V be the vector space of all sequences over R. Given (a1, a2, . . .) ∈ V , define
T, U : V → V by
T(a1, a2, a3, a4, . . .) = (a1, a3, a5, . . .) and U(a1, a2, a3, a4, . . .) = (0, a1, 0, a2, 0, a3, . . .)
(a) Find N(T) and N(U).
(b) Explain why T is onto, but not 1-1.
(c) Explain why U is 1-1, but not onto.

Answer 1

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