EXAM I SOLUTIONS
Math 51, Spring 2003. You have 2 hours. No notes, no books, no calculators. YOU MUST SHOW ALL WORK AND EXPLAIN ALL REASONING TO RECEIVE CREDIT Good luck! Name ID number
1.
(/20 points)
2.
(/15 points)
"On my honor, I have neither given no
EXAM I SOLUTIONS
Math 51, Spring 2001. You have 2 hours. No notes, no books. YOU MUST SHOW ALL WORK TO RECEIVE CREDIT Good luck! Name ID number
1.
(/20 points)
"On my honor, I have neither given nor received any aid on this examination. I have furthermore
FINAL EXAM SOLUTIONS
Math 51, Spring 2001. You have 3 hours. No notes, no books. YOU MUST SHOW ALL WORK AND EXPLAIN ALL REASONING TO RECEIVE CREDIT Good luck! Name ID number
1.
(/50 points)
On my honor, I have neither given nor received any aid on this ex
MATH 51 MIDTERM 1 SOLUTIONS (AUTUMN 2001)
2 1 123 1. Suppose u = 5, v = 0 , is the angle between them, and A = . 456 1 1 Compute: (a) (2 points) 2u 3v, 7 Solution. 2u 3v = 10 1 (b) (2 points) u v cos , v cos = u v = 1
Solution. u (c) (2 points) u
v sin ,
EXAM I SOLUTIONS
Math 51, Spring 2002. You have 2 hours. No notes, no books, no calculators. YOU MUST SHOW ALL WORK AND EXPLAIN ALL REASONING TO RECEIVE CREDIT Good luck! Name ID number
1.
(/20 points)
On my honor, I have neither given nor received any ai
Math 51 Midterm 2 Solutions
PROBLEM 1(a). A one-to one transformation must have null space cfw_0. The columns must be independent, there are pivots in every column, and no free variables, so the answer is rank (A) = n. PROBLEM 1(b). Onto means the column
Math 51, Spring 2007
Exam 1 Solutions April 24, 2007
Page 1 of 9
1. (10 points) Complete each of the following sentences. (a) A collection of vectors , . . . , is dened to be linearly independent if v1 vk (5 points) . . . the equation c1 + c2 + + ck = 0 v
Math 51, Winter 2007
Midterm 1 - Solutions
February 1, 2007
MIDTERM 1 - SOLUTIONS
Complete the following problems. You may use any result from class you like, but if you cite a theorem be sure to verify the hypotheses are satised. This is a closed-book,
MATH 51 MIDTERM
October 20, 2005 Name: Numeric Student ID: Instructors Name: I agree to abide by the terms of the honor code: Signature: Instructions: Print your name, student ID number and instructors name in the space provided. During the test you may n
Math 51 Midterm I Solutions
(These solutions are written more in the form of a guide to correct thinking, and a guide to the level of understanding we were trying to test. This is for students who want to learn from their mistakes and improve their unders