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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 straight-forward 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 take-home portion.
There will be an opportunity to make-up 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, 3rd 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 1-33 odd (34)
Tue Apr 7
Wed Apr 8
row reduction &
echelon forms
1.2 1-33 odd
Wed Apr 8
Thu Apr 9
vector equations 1.3 1-31 odd, 32
Fri Apr 10 the matrix equation
Ax = b
1.4 1-15 odd, 17-22, 23-31 odd,
32, 33, 35, (37, 39)
Mon Apr 13 solution sets of
linear systems
1.5 1-23 odd, 24, 26-33, 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 1-37 odd, 38, 39, 40, (41)
Thu Apr 16
Fri Apr 17
intro to linear
transformations
1.8 1-33 odd
Mon Apr 20 the matrix of a
linear
transformation
1.9 1-31 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 1-27 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 1-7 odd, 11, 13, 15-24, 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 1-7 odd, 11, 15, 16
Fri May 1 introduction to
determinants
3.1 1-41 odd
Mon May 4
Tue May 5
properties of
determinants
3.2 1-4, 5, 11, 15-20, 21, 25, 27,
29, 31, 32, 34, 39, 41
Tue May 5
Wed May 6
Cramer' s Rule ,
volume, & linear
transformations
3.3 1-9 odd, 13, 19, 25
Thu May 7
Fri May 8
vector spaces &
subspaces
4.1 1-23 odd, 31-33
Mon May 11
Tue May 12
null spaces, column
spaces, & linear
transformations
4.2 1-25 odd, 26-28, 31, 33-36
Tue May 12
Wed May 13
linearly independent
sets & bases
4.3 1-11 odd, 12-14, 15, 19,
21-27 odd, 31-34
Thu May 14 review    
Fri May 15 test two    
Mon May 18
Tue May 19
coordinate systems 4.4 1-15 odd, 16, 17, 21, 27, 29
Tue May 19
Wed May 20
dimension of a
vector space
4.5 1-23 odd, 27, 29, 31
Thu May 21 rank theorem 4.6 1-4, 5-31 odd

eigenvalues, eigenvectors, orthogonality, & quadratic forms

Fri May 22
Tue May 26
eigenvalues &
eigenvectors
5.1 1-9 odd, 13, 17, 19, 21, 23,
24, 25, 31, 33
Tue May 26
Wed May 27
the characteristic
equations
5.2 1-7 odd, 9, 15, 17, 21, 22
Thu May 28
Fri May 29
matrix
diagonalization
5.3 1-9 odd, 15-21 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 1-19 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
least-square
problems
6.5 3, 5, 7, 9, 13, 17, 25
Fri Jun 12 diagonalization of
symmetric matrices
7.1 1-11 odd, 13, 17, 23, 25, 29,
31
Mon Jun 15 quadratic forms 7.2 1-13 odd, 19, 21
Tue Jun 16 review    
Thu Jun 18 final exam
8:00-10:00
   
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