Math254OldQuiz2Sols

Math254OldQuiz2Sols - QUIZ 2 - SOLUTIONS MATH 254 - SUMMER...

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QUIZ 2 - SOLUTIONS MATH 254 - SUMMER 2001 - KUNIYUKI CHAPTER 4 1) 34 3 3 0 2 4 4 2 1 9 0 6 16 8 4 91 6 08 64 25 8 10 vw -= - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ - - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ = - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ - - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ = -- () - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ =- - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ 2) (Deleted) 3) The set (say, " W ") is a nonempty subset of R 5 ; 0 is guaranteed to be in it. Let x 1 and x 2 be any two members of W . Then, A x0 1 = , and A 2 = . Prove closure of W under vector addition: Show A xx 0 1 2 + = . AA A x x 00 0 1 2 1 2 + =+ = So, 1 2 + is in W . Prove closure of W under scalar multiplication: Let c be any real scalar. Show Ac 1 = . cA c 0 0 11 = = () = So, c x 1 is in W . Note: You could prove both types of closure simultaneously by showing xx0 1 2 + = . Therefore, W is a subspace of R 5 .
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4) a) The set of all polynomials in x whose degree is exactly three Yes No Note: The answer would have been "Yes" if the set were "The set of all polynomials in x with degree three or less, including 0." b) The set of all real 43 ¥ matrices Yes No c) The set of standard basis vectors in R 5 Yes No For example, 0 is not a standard basis vector.
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This note was uploaded on 09/08/2011 for the course MATH 254 taught by Professor Howard during the Spring '09 term at Mesa CC.

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Math254OldQuiz2Sols - QUIZ 2 - SOLUTIONS MATH 254 - SUMMER...

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