This one is going to take a lot of calculation. You might consider checking your work on something like Wolfram|Alpha. Only to check your work! You're on your honor. (Hey I managed it so you can too.)
In any way you feel like, find the matrix, A, that generates the following eigenvectors and their associated eigenvalues.
Find a formula for . and their eigenvectors and eigenvalues. (Hint: Consider even n and odd n. They have different formulas.)