Math254OldQuiz2

Math254OldQuiz2 - Math 254 Name: _ QUIZ 2 MATH 254 - SUMMER...

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Math 254 Name: ________________________ QUIZ 2 MATH 254 - SUMMER 2001 - KUNIYUKI CHAPTER 4 Show all appropriate work (as we have done in class) for full credit! A scientific calculator is allowed on this quiz. 1) If v = (3, 0, -2) and w = (-4, 2, 1), find 3 v - 4 w . (4 points) 2) (Deleted) (4 points) 3) Let A be a fixed 35 ¥ matrix. Prove that the set xx 0 O= {} RA 5 : is a subspace of R 5 by proving that it is closed under vector addition and scalar multiplication. (" O " means "is a member of") (8 points)
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4) For each of the following sets, circle "Yes" if it is a vector space, or circle "No" if it is not. Assume that the "standard" operations for vector addition and scalar multiplication are being used in each case. (20 points; 4 points each) a) The set of all polynomials in x whose degree is exactly three Yes No b) The set of all real 43 ¥ matrices Yes No c) The set of standard basis vectors in R 5 Yes No d) The set of all real 22 ¥ matrices in upper triangular form Yes No e) The set xx x ,, : 02 () {} is a real number Yes No
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Math254OldQuiz2 - Math 254 Name: _ QUIZ 2 MATH 254 - SUMMER...

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