Solutions to Axler, Linear Algebra Done Right 2nd Ed.
Edvard Fagerholm [email protected]_helsinki.|gmail.com
Beware of errors. I read the book and solved the exercises during spring break (one week), so the problems were solved in a hurry. However, if
Linear Algebra II
Math 306
Winter 2014
Professor Ben Richert
Exam 1
Solutions
Problem 1 (12pts) Denitions and theorems.
I. Denitions: Let V be a vector space over a eld F and cfw_ 1 , . . . , n V . Then we say . . .
v
v
(a3pts) spancfw_ 1 , . . . , n =
Linear Algebra II
Math 306
Winter 2014
Professor Ben Richert
Exam 2
Solutions
Problem 1 (12pts) Denitions. Let V, W be nite dimensional vector spaces over a eld F with dim V = n
and dim W = m, T : V W be a linear transformation, = cfw_ 1 , . . . , n be a
Math 306, Linear Algebra II, Winter 2014
Homework 1, due Friday 1/10
Read sections:
1. 1.1 and 1.2 (for 1/6)
2. 1.3 (for 1/9)
Do the following problems:
1. 1.2.12: A real-valued function f dened on the real line is called an even function if f (t) = f (t)
Math 306, Linear Algebra II, Winter 2014
Homework 5, due Friday 1/24
Read sections:
1. 1.6 (for 1/23)
2. 2.1 (for 1/23)
Do the following problems:
1. 1.6: 26, 31, 34
The grader will carefully consider 34 so you should write this one up more carefully.
Math 306, Linear Algebra II, Winter 2014
Homework 4, due Tuesday 1/21
Read sections:
1. 1.6 (for 1/17)
Do the following problems:
1. 1.5.2: Determine whether the following sets are linearly dependent or linearly independent.
(a)
1
2
3
4
,
2
4
6
8
in M22 (
Math 306, Linear Algebra II, Winter 2014
Homework 3, due Friday 1/17
Read sections:
1. 1.4 (for 1/14)
2. 1.5 (for 1/14)
Do the following problems:
1. 1.4.3: For each of the following lists of vectors in R3 , determine whether the rst vector can be express
Math 306, Linear Algebra II, Winter 2014
Homework 2, due Tuesday 1/14
Read sections:
1. 1.4 (for 1/10)
Do the following problems:
1. 1.3.8: Determine whether the following sets are subspaces of R3 under the operations of addition and
scalar multiplication
Math 306, Linear Algebra II, Winter 2014
Homework 6, due Tuesday 1/28
Read sections:
1. 2.1 (for 1/24)
Do the following problems:
1. 1.6: 10, 13
2. Lets explore the proof of the replacement theorem. Recall the statement: Let V be a v.s. with generating
se
Math 306, Linear Algebra II, Winter 2014
Homework 7, due Tuesday 2/4
Read sections:
1. 2.2 (for 2/3)
Do the following problems:
1. 2.1: 10, 12, 14, 28, 31
The grader will carefully consider 14a and 31a so you should write these up more carefully.
Math 306, Linear Algebra II, Winter 2014
Homework 12, due Tuesday 3/4
Read sections:
1. Read chapter 5.2 (for 2/28)
2. TBA
Do the following problems:
1. 5.2.4, 5.2.7, 5.2.12, 5.2.18
2. TBA
The grader will carefully consider TBA and TBA so you should write
Math 306, Linear Algebra II, Winter 2014
Homework 10, due Tuesday 2/18
Read sections:
1. Read chapter 4 (for 2/14).
2. Read chapter 5.1 (we might make it there by 2/14)
3. Read chapter 5.1 (for 2/18)
Do the following problems:
1. Let E be an elementary ma
Math 306, Linear Algebra II, Winter 2014
Homework 8, due Friday 2/7
Read sections:
1. 2.3 (for 2/4)
Do the following problems:
1. 2.2: 2, 3, 5, 8
2. Let V and W be n-dimensional vector spaces, and let T : V W be a linear transformation. Suppose
that is a
Math 306, Linear Algebra II, Winter 2014
Homework 9, due Friday 2/7
Read sections:
1. 2.4 (for 2/10)
2. 2.5 (for 2/11)
3. TBA
Do the following problems:
1. Let V and W be vector spaces and T L(V, W ) be an isomorphism. In class we show that the set map
T
STAT 312
Homework #4
Joey Roberts
STAT 312 Homework 4
5.2 A token ring local area network provides an intertoken time having a uniform distribution between 0 and 2
1.
seconds.
a. What is the probability that the time will be
a= 0
b= 2
f(x)= 0.5
1 Less tha