hello

i need help!!

can u guys show me the detail if possible ?

In each case below either show that the statement is True or give an example showing that it is False. (i) If U # R" is a subspace of R" and X + Y E U, then X and Y are both in U. (ii) If U is a subspace of R" and rX E U for all r E R, then X E U. (iii) If U is a subspace of R" and X E U, then - X E U. (iv) If X E U = span {Y, Z}, then U = span { X, Y, Z}. (v) If {x1, x2, ... k, Ck+1, . ..n) is a basis of R" and U = span {x1, ...ck} and V = span {ack+1 . ..n}, then UnV = {0}