This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MATH 51 FINAL EXAM December 11, 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. You have 3 hours to do all the problems. Question Score Maximum 1 14 2 10 3 16 4 12 5 14 6 10 7 12 8 12 9 10 10 18 11 10 12 10 13 10 14 15 15 15 16 12 Total 200 1 1. Let u 1 = 1 1 3 u 2 = 1 1 2 u 3 = 3 1 4 (a) (6 points) Find the dimension of span( u 1 , u 2 , u 3 ). (b) (8 points) Find all vectors v which are simultaneously orthogonal (i.e. perpen dicular) to all three vectors u 1 , u 2 and u 3 . 2. (10 points) Suppose B = ( x,y ) is a point on the circle of radius 1 centered at the origin. That is, x and y satisfy x 2 + y 2 = 1. Let A = ( 1 , 0), C = (1 , 0) and assume y 6 = 0 (so that B is not equal to A or C ). A B C Use dot products to show that angle ABC is a right angle. 3. Suppose A is a 5 5 matrix with rref( A ) = 1 0 1 4 0 0 1 2 3 0 0 0 0 1 0 0 0 0 0 0 0 0 For each part below, give the answer when possible. Otherwise answer not enoughFor each part below, give the answer when possible....
View
Full
Document
This note was uploaded on 08/16/2008 for the course MATH 51 taught by Professor Staff during the Spring '07 term at Stanford.
 Spring '07
 Staff
 Math, Linear Algebra, Algebra, Differential Calculus

Click to edit the document details