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Question

Consider R^3 with two orthonormal bases: the canonical basis e = (e1, e2, e3) and the basis f = (f1, f2, f3), where

f1 = 1/sqrt 3 (1,1,1), f2 = 1 /sqrt6 (1, -2, 1), f3 = 1/ sqrt2 (1, 0, -1).

Find the matrix, S, of the change of basis transformation such that [v]f = S[v]e, for all v belonging to R^3 , where [v]b denotes the column vector with the coordinates of the vector v in the basis b.