Question: D LT2: Let V be a vector space with basis B = {v1, ..., Un }. Let us define the linear transformation L; : V

D LT2: Let V be a vector space with basis B = {v1, ..., Un }. Let us define the linear transformation L; : V - R given by 1 i= j Now let T : V - R be an arbitrary linear transformation. Show that there exist @1, d2, . . ., an such that T = EjajLi and write the 01 , . .., an in terms of T and the basis vectors { v1 , . . ., Un}. [Hint: Maybe for v E V with _;_ bjv; = v, you can write down T(v) = >"_, bjT(v; ) and compare with writing the sum of Lj's]

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