# 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

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
 Prev Next

Start solving your Algebra Problems in next 5 minutes!

2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of February 23rd you will pay only \$39.99 instead of our regular price of \$74.99 -- this is \$35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1\$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:

Algebra Helper can solve problems in all the following areas:

• simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
• factoring and expanding expressions
• finding LCM and GCF
• (simplifying, rationalizing complex denominators...)
• solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
• solving a system of two and three linear equations (including Cramer's rule)
• graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
• graphing general functions
• operations with functions (composition, inverse, range, domain...)
• simplifying logarithms
• basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
• arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!