Suppose we have two bases v I, ... , Vn and WI, . .. , Wn for Rn. If a vector has

Chapter 7, Problem 36

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Suppose we have two bases v I, ... , Vn and WI, . .. , Wn for Rn. If a vector has coefficients bi in one basis and Ci in the other basis, what is the change of basis matrix in b = Me? Start from bivi ++bnvn = Vb =CIWI +",+cnwn = We. Your answer represents T(v) = v with input basis of v's and output basis of w's. Because of different bases, the matrix is not I

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