Let S be the subset of IR defined by 2 1 S = * = 20 2 E R3 : 1231 - 1211 -12:21= 0 2 3 Note that S contains the zero vector 0 . 1. EITHER state S is closed under vector addition by entering the word CLOSED in the answer box below OR show S is NOT closed under vector addition by specifying two different non-zero vectors x, y in S with integer coefficients which are not scalar multiples of each other such that such that x + y is not in S. Enter your answer in the box below using Maple notation, eg, enter , for x = C N , OAn 2. EITHER state S is closed under scalar multiplication by entering the word CLOSED in the answer box below OR show S is NOT closed under scalar multiplication by specifying (in this order) a non-zero vector x in S with integer components and an integer scalar _ such that the vector Ax is not in S. Enter your answer in the box below using Maple notation, e.g. enter , 4 for x = , 1 = 4 . CO N ,2 NOTE: The restriction to integers is to keep the arithmetic simple.)