Write H(n) for the n x n matrix whose entry in row i and column j is 1/(i + j).

a) Ask Maple to compute det(H(n)) when n = 10 and when n = 20. (Be careful, Maple may need double or triple precision.)
b) Find the largest eigenvalue and smallest eigenvalue of H(10) and H(20).
c) Try to find an eigenvector for each case of b) (four things to find).
d) Is the system H(n) = (0, 0, ....., 0, 1) solvable for n = 10 and n = 20?

Remarks: It may be helpful to start with n = 2 (by hand) and n = 3, 4, 5, 6 by Maple. Remember: Maple is graded, forms part of your final grade computation.