Needed as soon as possible only d and e needed

4. The Fibonacci sequence Fo. F1, . . . is defined by Fo = 0, F1 = 1, and Fn+2 = Fn + Fn+1. The first few terms of the sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, .... (a) Let g: R- -+ R' be the linear map given by Find the matrix G of the map g with respect to the standard basis. (b) Find the eigenvalues of G and a basis for R- consisting of eigenvectors of G. (c) Write the vector 9 as a linear combination of the eigenvectors from part (b). (d) Use the linear combination from part (c) to explicitly compute G"." (without actually computing the matrix ("). (e) Convince yourself (by testing a few examples) that Go . | = Then use your solution from part (d) to conclude that Fn = 2 " - ( 1 03 ) " )