Question: We knew that (V, W) is a vector space. Suppose that X is a subset of V (X may or may not be a subspace).

We knew that (V, W) is a vector space. Suppose that X is a subset of V (X may or may not be a subspace). Let U = {T E 130/, W) :T(x) = 0 , x E X}; so that U is the set ofall linear maps from V to W that are zero on vectors of X. a) Show that Ll is a subspace of (V, W). b) Let M = (X ), the subspace generated by X. Is it true that Whenever T E U then T(x) = I] for all x E M '

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