I need help with this question please.

2. Let U be a subspace of F defined by U = {(21, . .. , 26) ( F : 21 = 222, 23 = 424, 25 = 626} (Significance: Basis-identification, extension, direct sums) (a) (25 pts) Find a basis of U (b) (25 pts) Extend the basis in part (a) to a basis of F6 (c) (25 pts) Find a subspace W of F so that F6 = UO W (d) (25 pts) Is it possible to find a linear mapping T : F > F such that null(T) = W, and range(T) = W? Why/Why not? If it is possible, construct one such linear map