Question: Let R3 have the usual componentwise vector space operations. Let S be the subset of R3 defined by S: K: 3:2 9x23::c3a':1a:2:0 Note that 8

Let R3 have the usual componentwise vector space operations. Let S be the subset of R3 defined by S: K: 3:2 9x23::c3a':1a:2:0 Note that 8 contains the zero vector 0 . (a) EITHER state S is closed under vector addition by entering the word CLOSED in the answer box below OR show 5' is NOT closed under vector addition by specifying two different non-zero vectors x, y in S with integer components which are not scalar multiples of each other such that x + y is not in S. @ (b) EITHER state S is closed under scalar multiplication by entering the word CLOSED 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 A such that the vector Ax is not in S. IQ Let R3 have the usual componentwise vector space operations. Let S be the subset of R3 defined by S: x: :32 6R3:mmlm2=0 Note that 8 contains the zero vector 0 . (a) EITHER state S is closed under vector addition by entering the word CLOSED in the answer box below OR show 5' is NOT closed under vector addition by specifying two different non-zero vectors x, y in S with integer components which are not scalar multiples of each other such that x + y is not in S. @ (b) EITHER, state S is closed under scalar multiplication by entering the word CLOSED in the answer box below OR, show 3 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 A such that the vector Ax is not in S. IQ Let R3 have the usual componentwise vector space operations. Let S be the subset of R3 defined by S: x: :32 6R3:m3m1m%:0 Note that 8 contains the zero vector 0 . (a) EITHER state S is closed under vector addition by entering the word CLOSED in the answer box below OR show 8 is NOT closed under vector addition by specifying two different non-zero vectors x, y in S with integer components which are not scalar multiples of each other such that x l y is not in S. @ (b) EITHER state S is closed under scalar multiplication by entering the word CLOSED in the answer box below OR show 8 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 A such that the vector Ax is not in S. IQ Let {3 have the usual componentwise vector space operations. Let S be the subset of R3 defined by Note that 8 contains the zero vector 0 . (a) EITHER State 8 is closed under vector addition by entering the word CLOSED in the answer box below, OR show 3 is NOT closed under vector addition by specifying two different non-zero vectors x, y in S with integer components which are not scalar multiples of each other such that x + y is not in S. [E (b) 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

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