Dual Bases: Given a basis v1,..., vn of V, the dual basis L1,... , Ln of V* consists of the linear functions uniquely defined by the requirements

(a) Show that Li[v] = xi gives the ith coordinate of a vector v = x1v1 + ... + xnvn with respect to the given basis.
(b) Prove that the dual basis is indeed a basis for the dual vector space.
(c) Prove that if V = Rn and A = (v1 v2 ... vn) is the n × n matrix whose columns are the basis vectors, then the rows of the inverse matrix A-1 can be identified as the corresponding dual basis of (Rn)*.

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|1 i= j. |0, i +j. L,(v,) =