I'm not very good with subspaces...I'm trying to figure it out, but a little help would be nice on this problem (please don't just give the answers)

Find a basis for each of these subspaces ofR4:

a) all vectors whose components are equal

b) all vectors whose components add to zero (is this the nullspace?)

c) all vectors that are perpendicular to (1,1,0,0) and (1,0,1,1)

d) the column space (inR2) and nullspace (inR5) of U=

[1 0 1 0 1]

[0 1 0 1 0]