.
MAT2141: Quiz1. Answers.
P. J. Scott
Sept. 27, 2014
Due at the beginning of class, Monday, Sept. 29, 2014 .
1. Let V be a vector space and W V a subset of V. Assume it is possible to define a vector
space structure on W by defining some operations. Then
MAT 2141 Fall 2010
Assignment 6
Professor: Alistair Savage
Due date: December 2, 2010, 10:00am
You must justify all your answers in order to receive full marks.
Question 1 (4 points). Berberian, 3.6, Exercise 7. Let V be an n-dimensional vector space and
MAT 2141 - LINEAR ALGEBRA I
UNIVERSITY OF OTTAWA
ALISTAIR SAVAGE
Contents
About the course
Notation
1. Sets with operations (magmas)
1.1. Operations on sets
1.2. Use of parentheses
1.3. Identity elements
1.4. Invertible elements
1.5. Monoids
2. Fields
2.1
MAT 2141 Test 1
Oct. 20, 2005
Prof. P. J. Scott
In what follows, give full proofs and explanations of your answers.
1. Suppose W0 and W1 are subspaces of R4 , where the dimension of W0 = the dimension of
W1 = 3. Prove that W0 W1 = cfw_. In fact, what can
MAT 2141 Fall 2010
Assignment 5
Professor: Alistair Savage
Due date: November 18, 2010, 10:00am
You must justify all your answers in order to receive full marks.
Question 1 (3 points). Find a basis of the subspace
U = cfw_(x, y, z) R3 | x + 2y + 3z = 0
of
MAT 2141 Test 1 Answers
Oct. 19, 2006
Prof. P. J. Scott
In what follows, give full proofs and/or explanations of your answers.
1. Are the following statements true or false? If they are true, prove them. If they are false,
give a concrete counterexample.
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MAT 2141 Fall 2010
Assignment 4
Professor: Alistair Savage
Due date: November 4, 2010, 10:00am
You must justify all your answers in order to receive full marks.
Question 1 (4 points). Exercise 1 in Section 2.6 of the text (page 48): Prove that if V = M N
MAT 2141 Fall 2010
Assignment 1
Professor: Alistair Savage
Due date: September 16, 2010, 10:00am
You must justify all your answers in order to receive full marks.
Question 1 (3 points). Let E = cfw_1, 2, 3, 4 and dene an operation
1
2
3
4
1
1
1
1
2
2
1
2
.
MAT2141: Quiz1. True-false and multiple choice questions (typo
corrected)
P. J. Scott
Sept. 27, 2014
Due at the beginning of class, Monday, Sept. 29, 2014 .
1. Let V be a vector space and W V a subset of V. Assume it is possible to define a vector
space
MAT2141: Homework 3
Due Friday, 31 October. at 3:30 pm in the Box in the Math Department.
Remarks:
(i) Study my notes on the web, and the appropriate sections of the book, namely 2.52.7.
(ii) Study problem #9, p. 46. This is another importantfactorization
MAT2141: Homework 1
Due Friday, September 19, 2014 by 2:00 pm.
Remarks:
(i) Readings: My notes (on the web) and Chapter 1 of Berberian. Also look at the study problems
for DGD and class, on the web.
(ii) No late homeworks, please. The answers will be post
.
MAT2141: Homework 1 Answers
Due Friday, September 19, 2014 by 2:00 pm.
Remarks:
(i) Readings: My notes (on the web) and Chapter 1 of Berberian. Also look at the study problems
for DGD and class, on the web.
(ii) No late homeworks, please. The answers wi
MAT 2143, Winter 2015
1. (3 points) Determine whether or not the following relation is an equivalence relation on the
set Z of all integers.
m~ninZ ifmn>0
It is an equivalence relation (Y/N): (1)
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1. Let A Q R.
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2 b) If I E R, deﬁne what is meant by “l is the inﬁmum of A”, i.e. l = inf A.
2c) State necessary and sufﬁcient conditions for sup A t
MAT 2141 Final Exam
December 12, 2005
Prof. P. J. Scott
Give complete details and explain your reasoning fully.
Write neatly and clearly.
No notes or calculators permitted.
1. Let V be a vector space over F. Let T : V V be a linear map. Prove
T 2 = 0 (
MAT 2141 Fall 2010
Assignment 3
Professor: Alistair Savage
Due date: October 14, 2010, 10:00am
You must justify all your answers in order to receive full marks.
Question 1 (4 points). Exercise 6 in Section 2.2 of the text (page 31): Let P be the space of
MAT 2141 Fall 2010
Assignment 2
Professor: Alistair Savage
Due date: September 30, 2010, 10:00am
You must justify all your answers in order to receive full marks.
Question 1 (3 points). Suppose n N+ = cfw_1, 2, 3, . . . is not prime. Let Fn = cfw_0, 1, 2
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MAT 2141 Test 1 Answers
Oct. 19, 2006
Prof. P. J. Scott
In what follows, give full proofs and/or explanations of your answers.
1. Are the following statements true or false? If they are true, prove them. If they are false,
give a concrete counterexample.
MAT 2141 Fall 2010
Assignment 1 Solutions
Professor: Alistair Savage
Due date: September 16, 2010, 10:00am
You must justify all your answers in order to receive full marks.
Question 1 (3 points). Let E = cfw_1, 2, 3, 4 and dene an operation
1
2
3
4
1
1
1
MAT 2141: Linear Algebra I
Professor: Alistair Savage
Final Exam Solutions December 9, 2010
Surname
First Name
Student #
Instructions:
(a) You have 3 hours to complete this exam.
(b) The number of points available for each question is indicated in parenth
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