Question: Exercise 7. Let V be a nitedimensional vector space over IF. The vector space V* : (V, F) is called the dual of V. An

Exercise 7. Let V be a nitedimensional vector space over IF. The vector space V* : (V, F) is called the dual of V. An element of V* is thus a linear map f : V > IF, also known as a functional. (i) Let {U1,. .. ,vn} be a basis of V. Show that, for each i E {1, . . . ,n}, there exists a unique '03\" E V* satisfying 1 if 2' : j vi(vj)6i'{0 ifz'7j' Show that {01\

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