Question: 2. Let X be a vector space over a field K and let X' be the the set of linear functions from X to K,

2. Let X be a vector space over a field K and let X' be the the set of linear functions from X to K, also known as the dual space of X. (a) Let v1, . .., Un be a basis for X. For each i, show there exists a unique linear map fi : X - K such that fi(vi) = 1 and fi(v;) = 0 for j * i. (b) Show that f1, ..., In is a basis for X' (called the dual basis of v1, . . ., Un). (c) Consider the basis v1 = (1, -1, 3), v2 = (0, 1, -1), and v3 = (0, 3, -2) of X = 3. Find a formula for each element of the dual basis

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