1. Just plug in e1,e2,e3 into u. To get the columns of A.
2. Use GauB elimination to solve (A-I)x = 0
3. Use GauB elimination to solve Ax = 0
4. Show the determinant of the matrix with a,b,c as columns is non-zero or just use the fact that eigenvectors of different eigenvalues are always linear independant.
5. Since a,b,c are eigenvectors it's just a diagonal matrix with the corresponding eigenvalues as entries.
6. Note that Im(u) is the column space of D.
7. Follows trivially from the results of 2,3,4,6.
8. A = Q D Q^(-1) so A^n = Q D^n Q^(-1) where Q is the matrix with the eigenvectors you calculated in problem 2 and 3. Now D^n = D so you don't actually have to compute shit.
