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7. Let w E R be a fixed vector with |w| = 1 and let f : R3 -> R be the linear transformation given by f (v ) =v - 2(v . w)w. Let M be the standard matrix of f. Find two eigenvalues of M and show that M is diago- nalizable. 8. Let R2x2 be the vector space of 2 x 2 real matrices. A basis for R2x2 is Let f : R2x2 -> R be a linear transformation such that f(12) = 2 and f(AB) = f(BA) for any A, BER2x2. Use the above basis to prove that f(A) = 1,1 + 02,2 for any matrix A c R2x2