MATH 110 - Spring 2010 - Ribet - Midterm 1 (solution)

MATH 110 - Spring 2010 - Ribet - Midterm 1 (solution) -...

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Math 110 First Midterm Examination February 16, 2010 2:10–3:30 PM, 10 Evans Hall Please put away all books, calculators, and other portable electronic devices— anything with an ON/OFF switch. You may refer to a single 2-sided sheet of notes. For numerical questions, show your work but do not worry about simplifying answers. For proofs, write your arguments in complete sentences that explain what you are doing. Remember that your paper becomes your only representative after the exam is over. Problem Your score Possible points 1 5 points 2 12 points 3 6 points 4 7 points Total: 30 points 1. In R 3 , express (3 , 18 , - 11) as a linear combination of (1 , 2 , 3), ( - 2 , 0 , 3) and (2 , 4 , 1). This was a standard numerical problem of the type that most of you know how to do. The coefficients are: - 49 / 5, 3 and 47 / 5. I apologize for the fractions: I intended the answers to be whole numbers and must have mistyped. 2. Label each of the following statements as TRUE or FALSE. Along with your answer, provide an informal proof or an explanation. For false statements, an explicit counterexample might work best. In interpreting the statements, take v to be a vector, a to be a scalar, β to be a basis of V , etc., etc. Each part was worth 2 points. We gave out one point for the correct T/F answer and one point for the explanation. a. If av = v , then either a = 1 or v = 0. This is true, but a lot of you didn’t give a good reason. Since v = 1 · v , as proved in class, the equation av = v may be written ( a - 1) · v = 0. If the scalar a - 1 is non-zero, we may
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This note was uploaded on 07/03/2011 for the course MATH 110 taught by Professor Gurevitch during the Spring '08 term at University of California, Berkeley.

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MATH 110 - Spring 2010 - Ribet - Midterm 1 (solution) -...

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