Linear Algebra
Mathematics 220 is a one quarter introduction to linear algebra . The
principal topics include
solution of systems of linear equations, matrix algebra and determinants ,
abstract vector
spaces, eigen values and eigenvectors , inner product spaces, and quadratic forms .
The course
will probably make more sense if you can read or at least browse through the
relevant
sections of the book before each class. We'll spend a day or two discussing each
section of
the book.
I'll spend most of the class time explaining the concepts and presenting
examples showing
how the concepts are applied. I welcome questions at any time. There will be
portions of
class time where you get a chance to solve some problems.
This course is usually perceived to be very straightforward at the
beginning, but grows
more abstract and conceptually sophisticated. Keeping up with the new concepts
through
homework exercises is essential to success in the course. I may collect some
homework
exercises from the book, and additional problems. There may be occasional short
quizzes.
There will be three tests and a final exam. Some of the tests may have a
takehome portion.
There will be an opportunity to makeup one test by the way I score the final
exam. I look
at each section of the comprehensive final (a test one part, a test two part,
etc.) and look to
see on which section you have improved the most. If you have, for example,
improved the
most on the test two part of the final exam, then the score on the test two
portion of the
final replaces your original test two score. Of course, if the final exam scores are
all lower,
your original test scores are left un changed .
what you'll need
book: "Linear Algebra and its Applications" by David C. Lay, 3^{rd} ed. (updated),
Addison
Wesley, 2006.
prerequisite: Math 153 (calculus III) or concurrent
enrollment. What's essential is a
familiarity with vectors.
please turn o the sound on all cellphones, pagers, etc.
during class
grades
Each of the three tests will be worth 100 points and the
final exam will be worth 100 points,
and the quizzes and homework will count as a smaller number of points . The
course grade is
based on a percentage which may be calculated at any time. Add together all your
points.
Then divide by the sum of the possible points. Multiply by 100 for the course
percentage.
Course grades are then de termined by the fol lowing scale :
* A course percentage of at least 93%,
and a score of at least 90% on each test
earns a 4.0.
Other grades are linearly interpolated. For example, a
score of 85% corresponds to a grade
of 3.4.
test dates
test 1 
Wednesday, April 22 
test 2 
Friday, May 15 
test 3 
Monday, June 8 
final exam 
Thursday, June 18
8:00  10:00 
course outline
naturally the schedule is approximate
linear equation systems , vector & matrix equations,
linear independence, linear
transformations
Mon Apr 6 
systems of linear
equations 
1.1 
133 odd (34) 
Tue Apr 7
Wed Apr 8 
row reduction &
echelon forms 
1.2 
133 odd 
Wed Apr 8
Thu Apr 9 
vector equations 
1.3 
131 odd, 32 
Fri Apr 10 
the matrix equation
Ax = b 
1.4 
115 odd, 1722, 2331 odd,
32, 33, 35, (37, 39) 
Mon Apr 13 
solution sets of
linear systems 
1.5 
123 odd, 24, 2633, 35 
Tue Apr 14 
applications of
linear systems 
1.6 
1, 3, 5, 7, 11, 14 
1.10 
1, 3, 7, 9, (14) 
Wed Apr 15
Thu Apr 16 
linear independence 
1.7 
137 odd, 38, 39, 40, (41) 
Thu Apr 16
Fri Apr 17 
intro to linear
transformations 
1.8 
133 odd 
Mon Apr 20 
the matrix of a
linear
transformation 
1.9 
131 odd, 35 
Tue Apr 21 
review 


Wed Apr 22 
test one 


matrix algebra & determinants 
Thu Apr 23
Mon Apr 27 
matrix ope rations 
2.1 
127 odd 
Mon Apr 27
Tue Apr 28 
the inverse of a
matrix 
2.2 
1, 3, 5, 6, 7, 13, 15, 17, 18,
21, 22, 29, 35, 37 
Wed Apr 29 
characterizations of
invertible matrices 
2.3 
17 odd, 11, 13, 1524,
28,
29, 33, 35 
Thu Apr 30 
matrix
factorizations 
2.5 
1, 3, 11, 15, 25, 26, (31) 
Fri May 1 
applications to
computer graphics 
2.7 
17 odd, 11, 15, 16 
Fri May 1 
introduction to
determinants 
3.1 
141 odd 
Mon May 4
Tue May 5 
properties of
determinants 
3.2 
14, 5, 11, 1520, 21, 25, 27,
29, 31, 32, 34, 39, 41 
Tue May 5
Wed May 6 
Cramer' s Rule ,
volume, & linear
transformations 
3.3 
19 odd, 13, 19, 25 
Thu May 7
Fri May 8 
vector spaces &
subspaces 
4.1 
123 odd, 3133 
Mon May 11
Tue May 12 
null spaces, column
spaces, & linear
transformations 
4.2 
125 odd, 2628, 31, 3336 
Tue May 12
Wed May 13 
linearly independent
sets & bases 
4.3 
111 odd, 1214, 15, 19,
2127 odd, 3134 
Thu May 14 
review 


Fri May 15 
test two 


Mon May 18
Tue May 19 
coordinate systems 
4.4 
115 odd, 16, 17, 21, 27, 29 
Tue May 19
Wed May 20 
dimension of a
vector space 
4.5 
123 odd, 27, 29, 31 
Thu May 21 
rank theorem 
4.6 
14, 531 odd 
eigenvalues, eigenvectors, orthogonality, & quadratic
forms
Fri May 22
Tue May 26 
eigenvalues &
eigenvectors 
5.1 
19 odd, 13, 17, 19, 21, 23,
24, 25, 31, 33 
Tue May 26
Wed May 27 
the characteristic
equations 
5.2 
17 odd, 9, 15, 17, 21, 22 
Thu May 28
Fri May 29 
matrix
diagonalization 
5.3 
19 odd, 1521 odd, 25, 27,
29 
Mon Jun 1 
complex eigenvalues 
5.5 
1, 5, 9, 11, 13, 17 
Tue Jun 2
Wed Jun 3 
inner product 
6.1 
119 odd, 27, 28, 30 
Wed Jun 3
Thu Jun 4 
orthogonal sets 
6.2 
1, 3, 7, 9, 11, 13, 15, 17, 23,
27, 33 
Fri Jun 5 
review 


Mon Jun 8 
test three 


Tue Jun 9
Wed Jun 10 
orthogonal
projections 
6.3 
1, 5, 7, 9, 11, 15, 17, 21 
Wed Jun 10
Thu Jun 11 
leastsquare
problems 
6.5 
3, 5, 7, 9, 13, 17, 25 
Fri Jun 12 
diagonalization of
symmetric matrices 
7.1 
111 odd, 13, 17, 23, 25, 29,
31 
Mon Jun 15 
quadratic forms 
7.2 
113 odd, 19, 21 
Tue Jun 16 
review 


Thu Jun 18 
final exam
8:0010:00 


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