In each case either show that the statement is true or give an example showing that it is false.
(a) If U≠ Rn is a subspace of Rn and X+ Y is in U, then X and F are both in U.
(b) If U is a subspace of Rn and rX is in U for all r in R, then X is in U.
(c) If U is a subspace of Rn and X is in U, then -X is also in U.
(d) If X is in U and U = span{Y, Z}, then U = span{X, Y, Z}.
(e) The empty set of vectors in Rn is a subspace of Rn.
(f) [0 l]T is in span{[l 0]T, [2 0]T}.