Homework and Syllabus
Linear Algebra
MATH 2130 Summer 2018
Homework is due in class and must be stapled
with your name and homework number on it to
receive credit. You will be graded on the clarity of
your exposition.
Please read the suggested texts before class, and
then after class make sure to attempt the homework for the
sections we covered that day.
You may find it useful to use a computer algebra system to
check your matrix computations. The program Mathematica,
for instance, is available free to students via
the University of Colorado.
You may find the Mathematics
Academic Resource Center ("MARC" MATH 175) to be
useful as a meeting point for discussing homework.
An asterix * indicates that a homework assignment has not been finalized.
| Date | Topics | Reading | Homework |
| Monday June 4 |
Introduction to the
course, and overview of mathematical notation Sets, subsets, unions, intersections, products, equivalence relations, and maps. Matrix multiplication, and determinant and inverse formulas for small matrices. Introduction to LaTeX and Mathematica. |
You can read a bit about standard
mathematical language in: Richard Hammack, The Book of Proof, Creative Commons, 2nd Edition, 2013. Please see the references for LaTeX at the bottom of this webpage. If possible, bring a laptop with LaTeX installed. Here are some sample files we will use: .tex, .bib, .pdf. |
|
| Tuesday June
5 |
Linear equations in
linear algebra Systems of linear equations, row reduction, reduced row echelon form. |
D. Lay, S. Lay, and J. McDonald, Linear
Algebra and Its Applications (5th
Edition), Pearson, 2016 Section 1.1-2 |
|
| Wednesday June 6 |
Linear
equations in linear algebra continued. Vector equations, matrix equations, solution sets of linear systems, applications of linear systems. |
Lay Sections 1.3-6 |
|
| Thursday June 7 |
Linear
equations and linear algebra continued. Linear independence, introduction to linear transformations, the matrix of a linear transformation, linear models in business, science, and engineering. |
Lay Sections 1.7-10 |
|
| Friday June 8 |
Matrix
algebra Matrix operations, the inverse of a square matrix, characterizations of invertible matrices. |
Lay Sections 2.1-3 |
HW 1 Lay Section 1.1: 12, 15, 24. Section 1.2: 1, 5, 22. Section 1.3: 9, 24, 32, 34. Section 1.4: 11, 19, 24, 34. Section 1.5: 7, 24, 38. Section 1.6: 1, 3, 7. |
| Monday June 11 |
Matrix
algebra continued Partitioned matrices, matrix factorizations, the Leontief Input-Output model, applications to computer graphics. |
Lay Sections 2.4-7 |
|
| Tuesday June 12 |
Matrix
algebra continued Subspaces of real n-space, dimension and rank. |
Lay Sections 2.8-9 |
|
| Wednesday June 13 |
Determinants Introduction to determinants, properties of determinants, volume and linear transformations. |
Lay Sections 3.1-3 |
|
| Thursday June 14 |
Review | |
|
| Friday June 15 |
Review | Sample Midterm .pdf Solutions .pdf |
HW 2 Lay Section 1.7: 2, 6, 22. Section 1.8: 3, 22, 29. Section 1.9: 2, 3, 24. Section 1.10: 1, 5, 10. Section 2.1: 1, 16, 32. Section 2.2: 2, 5, 10. Section 2.3: 1, 4, 6, 12, 27. Section 2.4: 2, 5, 12. Section 2.5: 1, 24. Section 2.6: 1, 2, 11. Section 2.7: 1, 7, 11. |
| Monday June 18 |
MIDTERM | MIDTERM | MIDTERM |
| Tuesday June 19 |
Review of exam | ||
| Wednesday June 20 |
Vector
spaces Vector spaces and subspaces, linear transformations, kernel, null space, image. |
Lay Sections 4.1-2 You may also want to take a look at this .pdf |
|
| Thursday June 21 |
Vector
spaces continued Linearly independent sets, bases, coordinate systems. Dimension, rank, change of basis. |
Lay Sections 4.3-7 |
|
| Friday June 22 |
Vector
spaces continued Applications to difference equations, and Markov chains. |
Lay Sections 4.8-9 | HW 3 Lay Section 2.8: 5, 22. Section 2.9: 9, 18. Section 3.1: 2, 11, 15. Section 3.2: 2, 7, 28. Section 3.3: 1, 11, 23. Section 4.1: 2, 6, 24. Section 4.2: 2, 8, 26. Section 4.3: 4, 15, 22. Section 4.4: 2, 10, 18. |
| Monday June 25 |
Eigenvalues
and eigenvectors Eigenvalues and eigenvectors, the characteristic polynomial, diagonalization. |
Lay Sections 5.1-3 | |
| Tuesday June 26 |
Eigenvalues
and eigenvectors continued Eigenvectors and linear transformations, complex eigenvalues. |
Lay Sections 5.3-5 | |
| Wednesday June 27 |
Eigenvalues
and eigenvectors continued Discrete dynamical systems, applications to differential equations. |
Lay Sections 5.6-7 | |
| Thursday June 28 |
Orthogonality
and least squares Inner product, length, and orthogonality. |
Lay Section 6.1 |
|
| Friday June 29 |
Orthogonality
and least squares continued Orthogonal sets, orthogonal projections, Gram--Schmidt. |
Lay Sections 6.2-4 |
HW 4 Lay Section 4.5: 1, 9, 20. Section 4.6: 2, 13, 18. Section 4.7: 1, 6, 11. Section 4.8: 2, 5, 19. Section 4.9: 4, 10, 18. Section 5.1: 2, 7, 22. Section 5.2: 1, 9, 22. Section 5.3: 1, 5, 22. The following problems do not need to be turned in: Section 5.4: 2, 8, 9. Section 5.5: 1, 8, 23. |
| Monday July 2 |
Orthogonality
and least squares continued Least squares problems, applications to linear models. |
Lay Sections 6.5-6 |
|
| Tuesday July 3 |
Review |
||
| Wednesday July 4 |
NO
CLASS |
INDEPENDENCE DAY |
NO CLASS |
| Thursday
July 5 |
Review |
Sample final .pdf Solutions .pdf |
|
| Friday
July 6 |
FINAL EXAM In class (9:15 AM -- 10:50 AM in MUEN D144) |
FINAL EXAM |
HW 5 The following problems do not need to be turned in: Lay Section 5.6: 1, 3, 7. Section 5.7: 1, 3, 9. Section 6.1: 2, 9, 20. Section 6.2: 3, 8, 11. Section 6.3: 1, 17, 22. Section 6.4: 2, 14, 18. Section 6.5: 2, 5, 18. Section 6.6: 1, 2, 7. |
I strongly encourage
everyone to use LaTeX for typing homework. If you have
a mac,
one possible easy way to get started is with texshop.
If you are using linux,
there are a number of other possible ways to go, using
emacs, ghostview, etc. If you are using windows,
you're on your own, but I'm sure there's something online.
Here is a sample homework file to use: (the .tex
file, the .bib
file, and the .pdf
file). This site can help you find LaTeX symbols
by drawing: http://detexify.kirelabs.org/classify.html.
You may also want to try https://cocalc.com
(formerly https://cloud.sagemath.com/)
or https://www.sharelatex.com/
for a cloud version.