In each case, find a basis for the space V of all sequences [xn) satisfying the recurrence,

Question:

In each case, find a basis for the space V of all sequences [xn) satisfying the recurrence, and use it to find xn if x0 = 1, x1 = -1, and x2 = 1.
(a) xn+3 = -2xn + xn+1 + 2xn+2
(b) xn+3 = -6xn + 7xn+1
(c) xn+3 = -4xn + 3xn+2
(d) xn+3 = xn - 3xn+1 + 3xn+2
(e) xn+3 = 8xn - 12xn+l + 6xn+2