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7. (20 points) Let V = f(x0; x1; : : :) : xn+2 = (xn+1 + xn)=2g. (d) (4 points) Let  : V ! V be the shift map: (x0; x1; x2; : : :) = (x1; x2; : : :). Write the matrix representation of  using the basis (1; 0; :5; : : :) and (0; 1; :5; : : :). (e) (4 points) Determine the eigenvalues and eigenvectors of . Use these to diago- nalize the matrix representation found in the previous part. (f) (1 point) Describe the relationship between the solutions found in parts (b) and

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