Math 175, Fall 2010
H. Jordon
Solutions to Take-Home Exam 4
1. Let V = cfw_(a, b) | a, b R and dene the operations of vector addition and scalar
multiplication as follows:
(a, b) (c, d) = (a + c + 1, b + d 1)
and for a real number k ,
k (a, b) = (a, kb).
Name:
Math 175, Spring 2008
H. Jordon
Exam 1
106 points possible. 100 points maximum. Throughout this exam, R denotes the set of real numbers.
1. (18 pts.) Answer each of the following by CIRCLING True or False. No explanation necessary.
(a) True or False
Math 175, Spring 2008
H. Jordon
Answers to Exam 2
1. (a) True
(b) False
(c) False
(d) True
2. Any three of the following: columns of A are linearly independent, rank A = n, Ax = b has
at most one solution for every b Rn , nullity A = 0, rref(A) has a pivo
Name:
Math 175, Spring 2008
H. Jordon
Exam 2
100 points possible. Throughout this exam, R denotes the set of real numbers.
1. (12 pts.) Answer each of the following by CIRCLING True or False. No explanation necessary.
(a) True or False: If T : Rn Rm is a
Name:
Math 175, Spring 2008
H. Jordon
Exam 3
104 points possible. 100 points maximum. Throughout this exam, R denotes the set of real numbers.
1. (12 pts.) Answer each of the following by CIRCLING True or False. No explanation necessary.
(a) True or False
Math 175, Spring 2008
H. Jordon
Answers to Exam 4
1. (a) True
(b) False
(c) False
(d) False
2. Let u = (a, b) where a, b R. Then (k +)u = (k +)a, b) = (ka+a, b) and (k u)(u) =
(ka, b) (a, b) = (ka + a, 2b) so scalar multiplication does not distribute over
Name:
Math 175, Spring 2008
H. Jordon
Exam 4
100 points maximum. Throughout this exam, R denotes the set of real numbers.
1. (12 pts.) Answer each of the following by CIRCLING True or False. No explanation necessary.
(a) True or False: Let A be an inverti
Math 175, Fall 2010
H. Jordon
Study Guide for Exam 1
In what follows is a brief synopsis of what we have covered in Chapter 1, Sections 1-4, 6. Use this
list a guide to help you make up your own study guide.
On the exam, you can expect several proofs, TRU
Math 175, Fall 2010
H. Jordon
Study Guide for Exam 2
In what follows is a brief synopsis of what we have covered in Sections 1.7, 2.1, 2.3, 2.4, 2.7, 2.8.
Use this list a guide to help you make up your own study guide.
On the exam, you can expect several
Math 175, Fall 2010
H. Jordon
Study Guide for Exam 3
In what follows is a brief synopsis of what we have covered in Sections 3.1, 3.2, 4.14.5. Use this
list a guide to help you make up your own study guide.
On the exam, you can expect several proofs, TRUE
Math 175, Fall 2010
H. Jordon
Study Guide for Exam 4
In what follows is a brief synopsis of what we have covered in Sections 5.15.3, 7.17.3. Use this
list a guide to help you make up your own study guide.
On the exam, you can expect several proofs, TRUE/F
Math 175
H. Jordon
Answers to Exam 1
1. (a) False
(b) False
(c) False
(d) False
(e) True
(f) False
2. Let A = 1 a2 . . . an ] and let B = [b1 b2 . . . bn ] where ai and bi are m 1 columns. Let
[a
u1
u2
u = . where ui is a scalar. Then
.
.
un
(A + B )u =