In each case determine whether U is a subspace of R3. Support your answer.
(a) U = {[1 s t]T | s and t in R}.
(b) U = {[0 s t]T | s and t in R}.
(c) U = {[r s t]T | r, s, and t in R, - r + 3s + 2t = 0}.
(d) U = {[r 3s r - 2]T | r and s in R}.
(e) U = {[r 0 s]T | r2 + s2 = 0, r and s in R}.
(f) U = {[2r -s2 r]T| r, s, and t in R}.