Question: Let R3 have the usual componentwise vector space operations. Let S be the subset of R3 defined by $1 3: 3:: m2 6R3 :m3iz1 793%

Let R3 have the usual componentwise vector space operations. Let S be the subset of R3 defined by $1 3: 3:: m2 6R3 :m3iz1 793% :0 m3 Note that 3 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 Sis NOT closed under vector addition by specifying two different nonzero vectors x, y in S with integer coefficients which are not scalar multiples of each other such that x + y is not in S. 1 4 Enter your answer in the box below using Maple notation, e.g. , for x : 2 , y : 5 3 6 , . E] El 2. EITHER state S is closed under scalar multiplication by entering the word CLOSED in the answer box below OR show .5' 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'. Enteryour answer in the box below using Maple notation, e.g. , 4 for x = 2 , A = 4. ,2 O E! El

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