math54-Spring_07-mt1-Ribet-soln

math54-Spring_07-mt1-Ribet-soln - Math 54 Professor K A...

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Unformatted text preview: Math 54 Professor K. A. Ribet Midterm Exam February 14, 2007 This exam was an 80-minute exam. It began at 3:40PM. There were 4 problems, for which the point counts were 7, 12, 7 and 4. The maximum possible score was 30. 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. When you answer questions, explain in words what you are doing: your paper is your ambassador when it is graded. Correct answers without appropriate supporting work will be regarded with great skepticism. Incorrect answers without appropriate supporting work will receive no partial credit. Please write your name on each page of this exam. At the conclusion, please hand in your paper to your GSI. 1. Label the following statements as TRUE or FALSE, giving a short justification for your choice. There are six parts to this problem, two per page. a. If the span of v 1 ,...,v n contains w 1 , w 2 and w 3 , it contains the span of these three vectors. This is true: see (3.33) on page 173 of the textbook. b. If B is an n × 5 matrix, the set of matrices A ∈ M mn such that AB = 0 is a subspace of M mn ....
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math54-Spring_07-mt1-Ribet-soln - Math 54 Professor K A...

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