Math254Mid2

# Math254Mid2 - Math 254 Name: _ MIDTERM 2 MATH 254 - SUMMER...

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Math 254 Name: ________________________ MIDTERM 2 MATH 254 - SUMMER 2002 - KUNIYUKI CHAPTERS 4, 5 GRADED OUT OF 75 POINTS ¥ 2 = 150 POINTS TOTAL Circle your final answers! Show all work and simplify wherever appropriate, as we have done in class! A scientific calculator is allowed on this exam. Assume that the "standard" operations for vector addition and scalar multiplication are being used in all relevant problems. 1) For each set below, circle "Yes" if it is a vector space, or circle "No" if it is not. Whenever you answer “Yes”, you do not have to justify your answer. • Whenever you answer “No”, give a counterexample. (10 points total) a) The set xy x y , () {} is an integer and is a real number Yes No b) The set of all fourth-degree polynomials in x Yes No c) Span , , 123 vvv , where v 1 , v 2 , and v 3 are vectors in R 6 Yes No

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2) Let W be the set of all 33 ¥ real diagonal matrices. Prove that W is a subspace of M , . You may assume that M , is, itself, a vector space without having to prove that. (Completeness and quality are criteria for grading your proof.)
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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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Math254Mid2 - Math 254 Name: _ MIDTERM 2 MATH 254 - SUMMER...

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