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00aut-m1 - MATH 51 MIDTERM 1 Levandosky 11 15 11:00 1:15...

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MATH 51 MIDTERM 1 October 19, 2000 Brumfiel Hutchings Levandosky Staffilani White 11:00 01 05 09 13 17 1:15 03 07 11 15 19 Name: Student ID: Signature: Instructions: Print your name and student ID number and write your signature to indicate that you accept the honor code. Circle the number of the section for which you are registered on Infopier. During the test, you may not use notes, books, or calculators. Read each question carefully, and show all your work. Put a box around your final answer to each question. Each of the ten problems is worth 10 points. You have 90 minutes to do all the problems. Question Score 1 2 3 4 5 6 7 8 9 10 Total 1. Find all solutions of the following system: x 1 + x 2 + x 4 = 7 x 1 + x 2 + x 3 + x 4 = 10 x 1 + x 3 + x 4 = 9 1
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2. Let L be the intersection of the two planes x + 2 y + 3 z = 10 and 4 x + 5 y + 6 z = 28 . Find a parametric equation for L . 3. (a) Suppose u and v are vectors in R n such that u + v and u - v are orthogonal (i.e., perpendicular) to each other. Show that k u k = k v k .
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