Question: Theorem 2.10. Let V be a vector space. Let T, U1, U2 E C(V). Then (a T(U1 + U2) = TU1 + TU2 and (U1

Theorem 2.10. Let V be a vector space. Let T, U1, U2 E C(V). Then (a T(U1 + U2) = TU1 + TU2 and (U1 + U2) T = UIT + U2 T (b) T(U1 U2) = (TU1) U2 (C) TI = IT = T (d) a(U1U2) = (aU1)U2 = U1(aU2) for all scalars a.8. Prove Theorem 2.10. Now state and prove a more general result involv- ing linear transformations with domains unequal to their codomains

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