Homework 4 - Math 102
Sections 2.4 - 2.6
Due by 2pm Friday, August 16 to the dropbox in the basement of APM.
1. 2.5 #8 This problem concerns the following graph.
1
e1
e5
e4
4
e2
e6
3
e3
2
Write down t
Homework 5 - Math 102
Sections 3.1 - 3.3
Due by 5pm Tuesday, August 20 to the dropbox in the basement of APM.
1
4
1. Find the projection p of b = 4 onto the line through 4 and the projection matrix P
Homework 5 - Math 102
Sections 3.1 - 3.3
Due by 5pm Tuesday, August 20 to the dropbox in the basement of APM.
1
4
1. Find the projection p of b = 4 onto the line through 4 and the projection matrix P
Homework 2 - Math 102
Due by 5pm Thursday, August 8 to the dropbox in the basement of APM.
1. Show that the product of two upper triangular matrices is upper triangular. That is, if A and B are
upper
Homework 6 - Math 102
Sections 3.3 - 3.4
Due by 2pm Friday, August 23 to the dropbox in the basement of APM.
0
1
0
1
1. 3.3 #12 If V is the subspace spanned by
0 and 1
0
1
nd
(a) a basis for the or
Homework 6 Solutions
0
1
0
1
1. 3.3 #12 If V is the subspace spanned by
0 and 1
0
1
nd
(a) a basis for the orthogonal complement V .
(b) the projection matrix P onto V .
0
1
(c) the vector in V clo
Homework 7 - Math 102
Chapter 4
Due by 5pm Tuesday, August 27 to the dropbox in the basement of APM.
11
21
1. Find the determinant of A =
31
41
12
22
32
42
13
23
33
43
14
24
. Theres a smart way t
Homework 7 Solutions
11
21
1. Find the determinant of A =
31
41
12
22
32
42
13
23
33
43
14
24
. Theres a smart way to do this!
34
44
Solution: Recall that the row operation add a multiple of one
Homework 8 - Math 102
Sections 5.1-5.3
Due by 2pm Friday, August 30 to the dropbox in the basement of APM.
1. The characteristic polynomial of a matrix A is a polynomial in ,
p() = cn n + cn1 n1 + + c
Using the Singular Value Decomposition for Image Compression
In this project, youll explore an application of a certain matrix decomposition, called the singular value
decomposition (SVD), to image co
Least Squares
In this project, we will investigate the problem of tting a curve to some data points using the method of
least squares. Our approach will be dierent than the one learned in class, but o
Google Page Rank
In this project, we will learn the basics behind Googles Page Rank algorithm, which is used to provide
search engine users with relevant search results. The content of this project wi
Homework 4 - Math 102
Sections 2.4 - 2.6
Due by 2pm Friday, August 16 to the dropbox in the basement of APM.
1. 2.5 #8 This problem concerns the following graph.
1
e1
e5
e4
e2
e6
4
3
e3
2
Write down t
Homework 3 Solutions- Math 102
1. (a) Compute the matrix products P A and DA. Notice how multiplying on the left by a permutation
matrix or a diagonal matrix changes the rows of A.
20 0
010
1 1 3
4
2
Homework 3 - Math 102
Due by 5pm Tuesday, August 13 to the dropbox in the basement of APM.
1. (a) Compute the matrix products P A and DA. Notice how multiplying on the left by a permutation
matrix or
1.
2.
t - h N : l
The following foreign exchange rates were printed in the newspaper, where
1; denotes US dollars, J denotes Jodanian diners, and M denotes German mark .
_d.l_ = 9.11.! __C
Syllabus for Math 102
Summer Session II, 2013
Course:
Math 102 (Applied Linear Algebra)
Credit Hours:
4
Prerequisites:
Math 20F or Math 31AH
Summary:
This course is a sequel to 20F, intended to give y
Name
PID
Practice Midterm Exam - Math 102
70 minutes
The test covers sections 1.1 through 3.4 of your textbook, excluding section 1.7.
The actual midterm is on Thursday during class - please bring a
Name
PID
Practice Final Exam - Math 102
3 hours
The test is cumulative, though more emphasis will be placed on later material.
The nal is on Friday from 11:30 to 2:30 - please bring a blue book.
I
Homework 9 - Math 102
Sections 5.5-5.6
Due by 5pm Tuesday, September 3 to the dropbox in the basement of APM.
1. Explain why
3
0
0
4
is similar to
3
0
1
4
but
B=
0
i
E=
4
3+i
3i
6
3
0
0
3
2.
A=
1
1
0
Homework 9 Solutions
1. Explain why
3
0
0
4
is similar to
3
0
1
4
3
0
but
0
3
3
0
is not similar to
1
3
.
30
31
31
is similar to
because
is diagonalizable. It has two dierent
04
04
04
eigenvalues and
Homework 8 - Math 102
Sections 5.1-5.3
Due by 2pm Friday, August 30 to the dropbox in the basement of APM.
1. The characteristic polynomial of a matrix A is a polynomial in ,
p() = cn n + cn1 n1 + + c
Homework 1 Solutions - Math 102
These are the denitions of the terms you were asked to dene in Homework 1. You should use
these denitions to study for Thursdays quiz.
A linear system of equations is a
Homework 10 - Math 102
Sections 6.1-6.3
Due by 3pm Friday, September 6 to the dropbox in the basement of APM.
1. 6.2 #4: Show from the eigenvalues that if A is positive denite, so is A2 and so is A1 .
Homework 1 - Math 102
Due by 5pm Tuesday, August 6 to the dropbox in the basement of APM.
On a separate piece of paper, write the denition of each term.
You should try lling in what you remember witho
Homework 2 Solutions- Math 102
1. Show that the product of two upper triangular matrices is upper triangular. That is, if A and B are
upper triangular, show
(AB )ij = 0 if i > j.
Similarly, show that
Computer Graphics
In this project, we will see how linear algebra can be used in computer graphics. We wont do any
programming, but we will answer the types of questions that someone who was programmi