Answer to Question #95867 in Linear Algebra for Ananna Mitra

Question

Suppose T : V → V is linear and let W be a subspace of V . Further suppose that
T(w) ∈ W for all w ∈ W. Let S : W → W be defined by S(w) = T(w).

(a) Find an example of such a T and {0} 6= W 6= V when V = R
2
.
(b) Prove (in general) that N(S) = N(T) ∩ W.

Answer 1

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