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Unformatted text preview: (d) Let S be the set of vectors [ x, y ] satisfying xy = 0. Then S is not closed under addition of vectors. For example [1 , 0] S and [0 , 1] S , but [1 , 0] + [0 , 1] = [1 , 1] 6 S . (e) Let S be the set of vectors [ x, y ] satisfying x 0 and y 0. Then S is not closed under scalar multiplication. For example [1 , 0] S and-1 R , but (-1)[1 , 0] = [-1 , 0] 6 S . 2. Let X, Y, Z be vectors in R n . Then by Lemma 3.2.1 h X + Y, X + Z, Y + Z i h X, Y, Z i , as each of X + Y, X + Z, Y + Z is a linear combination of X, Y, Z . 30...
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This note was uploaded on 12/19/2011 for the course MAS 3105 taught by Professor Dreibelbis during the Fall '10 term at UNF.
- Fall '10