Let U and V be vector spaces, and let L(V,U) be the set of all
linear...
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Let U and V be vector spaces, and let L(V,U) be the set of alllinear transformations from V to U. Let T_1 and T_2 be inL(V,U),v be in V, and x a real number. Definevector addition in L(V,U) by(T_1+T_2)(v)=T_1(v)+T_2(v), and define scalar multiplication of linear maps as(xT)(v)=xT(v). Show that underthese operations, L(V,U) is a vector space.
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