Homework and Syllabus
Linear Algebra
MATH 2130 Spring 2021
Homework must be submitted via Canvas, and
is due at the start
of class, with your name and homework
number on
it to receive credit. You will be graded on the
clarity of your exposition. Messy, disorganized, or
poorly written assignments will not receive credit.
Starting with Homework 3,
all assignments must be written in LaTeX.
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 Math Academic Resource Center ("MARC" online) to be useful as a virtual meeting point for discussing homework, and a place to get some further help understanding the material.
An asterix * indicates that a homework assignment has not been finalized.
| Date | Topics |
Reading |
Homework |
| L1 Friday January 15 | Introduction to the course, and
overview of mathematical notation A brief review of some mathematical notation, including sets, subsets, unions, intersections, products, and maps. Matrix addition and multiplication, and determinant and inverse formulas for small matrices. |
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. You may also want to take a look at The Not So Short Introduction to LaTeX 2e |
|
| Monday January 18 |
MLK
DAY |
NO CLASS |
NO CLASS |
| L2 Wednesday January 20 |
Introduction
to LaTeX |
If possible, make
sure you already have LaTeX installed. See the
bottom of this page. Here are some sample files we will use: .tex, .bib, .pdf Kate Stange has the following tutorial for getting started with LaTeX. |
|
| L3 Friday January 22 |
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 Here are some slides on the Reduced Row Echelon form of a matrix. Kate Stange has some very useful comments about doing homework. |
HW 1 5 points extra credit for typing in LaTeX. You must upload both your .pdf and .tex files to Canvas to receive extra credit. Hammack Chapter 12 Section 12.1: 4,6. Section 12.2: 5,10,16. Section 12.4: 2,6,10. Section 12.5: 2,8. |
| L4 Monday
January 25 |
Linear equations in
linear algebra continued. Vector equations, span, matrix equations, solution sets of linear systems. |
Lay Sections 1.3-5 | |
| L5 Wednesday
January 27 |
Linear equations in
linear algebra continued. Solution sets of linear systems, applications of linear systems (1.6). |
Lay Sections 1.5-6 | |
| L6 Friday
January 29 |
Linear equations and
linear algebra continued. Linear independence, introduction to linear transformations, the matrix of a linear transformation. |
Lay Sections 1.7-9 | HW 2 5 points extra credit for typing in LaTeX. You must upload both your .pdf and .tex files to Canvas to receive extra credit. 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. |
| L7 Monday February 1 |
Linear
equations and linear algebra continued. The matrix of a linear transformation, linear models in business, science, and engineering (1.10). |
Lay Sections 1.9-10 | |
| L8 Wednesday February 3 |
Matrix
algebra Matrix operations, the inverse of a square matrix, characterizations of invertible matrices. |
Lay Sections 2.1-3 | |
| L9 Friday February 5 |
Matrix
algebra continued Subspaces of real n-space, dimension and rank. |
Lay Sections 2.8-9 |
HW 3 You must upload both your .pdf and .tex files to Canvas. Lay Section 1.7: 2, 6, 22. Section 1.8: 3, 22, 29. Section 1.9: 2, 3, 24. Section 1.10: 1, 10. Section 2.1: 1, 16, 32. Section 2.2: 2, 5, 10. Section 2.3: 1, 4, 6, 12, 27. |
| L10 Monday February 8 |
Review |
||
| L11 Wednesday February 10 |
Review |
Practice exam and solutions. Kate Stange has some very useful comments about math anxiety. |
|
| Friday February 12 |
MIDTERM I | MIDTERM I |
MIDTERM I |
| L12 Monday February 15 |
Matrix
algebra continued Partitioned matrices, matrix factorizations (2.5), the Leontief Input-Output model (2.6), applications to computer graphics (2.7). |
Lay Sections 2.4-7 | |
| L13 Wednesday February 17 |
WELLNESS
DAY |
NO CLASS |
NO CLASS |
| L14 Friday February 19 |
Review Midterm I | HW 4 Lay Section 2.4: 2, 5, 12. Section 2.5: 1, 24. Section 2.8: 5, 22. Section 2.9: 9, 18. |
|
| L15
Monday February 22 |
Determinants Introduction to determinants, properties of determinants, volume and linear transformations (3.3). |
Lay Sections 3.1-3 | |
| L16
Wednesday February 24 |
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 |
|
| L17
Friday February 26 |
Vector spaces continued Linearly independent sets, bases, coordinate systems. Dimension. |
Lay Sections 4.3-5 | HW 5 Lay Section 2.6: 1, 2, 11. Section 2.7: 1, 7, 11. Section 3.1: 2, 11, 15. Section 3.2: 2, 7, 28. Section 3.3: 1, 11, 23. |
| L18 Monday March 1 |
Vector
spaces continued Dimension, rank, change of basis. |
Lay Sections 4.5-7 | |
| L19 Wednesday March 3 |
Vector
spaces continued Applications to difference equations (4.8), and Markov chains (4.9). |
Lay Sections 4.8-9 | |
| L20 Friday March 5 |
Eigenvalues
and eigenvectors Eigenvalues and eigenvectors, the characteristic polynomial, diagonalization. |
Lay Sections 5.1-3 | HW 6 Lay Section 4.1: 2, 6, 24. Section 4.2: 2, 8, 26. Section 4.3: 4, 15, 22. Section 4.4: 2, 10, 18. Section 4.5: 1, 9, 20. Section 4.6: 2, 13, 18. Section 4.7: 1, 6, 11. |
| L21
Monday March 8 |
Eigenvalues and
eigenvectors continued Diagonalization. |
Lay Section 5.3 | |
| L22
Wednesday March 10 |
Eigenvalues and
eigenvectors continued Eigenvectors and linear transformations, complex eigenvalues. |
Lay Sections 5.4-5 | |
| L23 Friday March 12 | Eigenvalues
and eigenvectors continued Discrete dynamical systems (5.6), applications to differential equations (5.7). |
Lay Sections 5.6-7 | HW 7 Lay 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. Section 5.4: 2, 8, 9. Section 5.5: 1, 8, 23. |
| L24 Monday March 15 | Review |
||
| L25 Wednesday March 17 |
Review |
Practice exam and solutions. | |
| Friday March 19 |
MIDTERM
II |
MIDTERM II |
|
| L26 Monday March 22 | SPRING PAUSE Review Midterm II |
SPRING PAUSE |
SPRING PAUSE |
| L27 Wednesday March 24 | SPRING PAUSE Applications of linear algebra |
SPRING PAUSE |
SPRING PAUSE |
| L28 Friday March 26 | SPRING PAUSE Applications of linear algebra |
SPRING PAUSE |
SPRING PAUSE |
| L29
Monday March 29 |
Orthogonality and least
squares Inner product, length, and orthogonality. |
Lay Section 6.1 | |
| L30
Wednesday March 31 |
Orthogonality and least
squares continued Orthogonal sets, orthogonal projections. |
Lay Sections 6.2-3 | |
| L31
Friday April 2 |
Orthogonality and least
squares continued Gram--Schmidt. |
Lay Sections 6.4 | HW 8 Lay Section 5.6: 1, 7. Section 5.7: 1, 9. Section 6.1: 2, 20. Section 6.2: 3, 11. Section 6.3: 1, 22. |
| L32 Monday April 5 |
Orthogonality
and least squares continued Least squares problems. |
Lay Section 6.5 | |
| L33 Wednesday April 7 |
Orthogonality
and least squares continued Applications to linear models (6.6). |
Lay Section 6.6 | |
| L34 Friday April 9 |
Orthogonality
and least squares continued Inner product spaces |
Lay Section 6.7 |
HW 9 Lay Section 6.4: 2, 18. Section 6.5: 2, 18. Section 6.6: 1, 7. |
| L35
Monday April 12 |
Orthogonality and least
squares continued Applications of inner product spaces |
Lay Section 6.8 |
|
| L36
Wednesday April 14 |
Symmetric matrices and
quadratic forms Diagonalization of symmetric matrices |
Lay Section 7.1 |
|
| L37
Friday April 16 |
Symmetric matrices and
quadratic forms continued Quadratic forms |
Lay Section 7.2 |
HW 10 Lay Section 6.7: 9. Section 6.8: 1. Section 7.1: 2, 8, 25. |
| L39 Monday April 19 |
Symmetric
matrices and quadratic forms continued Constrained optimization |
Lay Section 7.3 | |
| L39 Wednesday April 21 |
Symmetric
matrices and quadratic forms continued Singular Value Decomposition |
Lay Section 7.4 |
|
| L40 Friday April 23 |
Symmetric
matrices and quadratic forms continued Applications to image processing and statistics |
Lay Section 7.5 |
HW 11 Lay Section 7.2: 1, 5. Section 7.3: 3. Section 7.4: 2, 8. |
| L41 Monday April 26 | Review |
Practice exam and solutions. |
|
| L42
Wednesday April 28 |
Review |
||
| Friday April 30 | READING DAY |
NO CLASS |
NO CLASS |
| Saturday
May 1 |
FINAL
EXAM 4:30 - 7:00 PM |
FINAL EXAM |
FINAL EXAM |
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.overleaf.com
(formerly https://www.sharelatex.com/)
for a cloud version.