In Problems 29 and 30, solve the given initial-value problem.
29. x' = ([2,4],[-1,6])x, x(0) = ([-1],[6])
30. x' = ([0,0,1],[0,1,0],[1,0,0])x, x(0) = ([1],[2],[5])
31. Show that the 5x5 matrix
A = ([2,1,0,0,0],[0,2,0,0,0],[0,0,2,0,0],[0,0,0,2,1],[0,0,0,0,2])
has an eigenvalue λ(1) of multiplicity 5. Show that three linearly independent eigenvectors corresponding to λ(1) can be found.