Math254OldQuiz3 - Math 254 Name QUIZ 3 MATH 254 SUMMER 2001...

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Math 254 Name: ________________________ QUIZ 3 MATH 254 - SUMMER 2001 - KUNIYUKI CHAPTERS 5, 6 Show all appropriate work (as we have done in class) for full credit! A scientific calculator is allowed on this quiz. You do not have to rationalize denominators or simplify radicals (e.g., 12 2 3 = ). 1) If v = (4, 2, -3), find the unit vector in the direction of v . In other words, normalize v . (5 points) 2) Find the angle between the vectors v = (3, 1, 0) and w = (2, -3, 5). Indicate whether your final answer is in degrees or in radians. If you are using degrees, round off your answer to the nearest hundredth of a degree; if you are using radians, round off your answer to three decimal places. (15 points)
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3) If v and w are orthogonal vectors, what must be their dot product? (2 points) 4) The set of vectors below is a basis for a two-dimensional subspace of R 3 . Use the Gram-Schmidt orthonormalization process to transform this basis 3 4 5 3 14 7 - - - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ È Î Í Í Í ˘ ˚ ˙ ˙ ˙ Ï Ì Ô Ó Ô ¸ ˝ Ô ˛ Ô , into an orthonormal basis for the same subspace. (25 points)
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5) The set b b 1 2 , { } is a basis for R 2 . Let T R R : 2 2 Æ be a linear transformation such that
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