MATH 321 section 1: Introduction to Linear Algebra
MATH 321 section 1 Homepage

Welcome, please note that the offical syllabus is linked here. Please note this webpage is where test reviews, solutions and lecture notes are posted. For your convenience,


I. Course Contact Information:


II. Useful Materials and Links:
  1. Course Syllabus
  2. Brief Unofficial Syllabus:
    3 Tests(1500pts each),
    Weekly Homework(500pts),
    Quizzes(500pts),
    4 Problem Sets(1500pts total),
    Final (3000pts).
    Bonus work available,
    class attendance is expected.
    Keeping up to date on definitions and homework expected,
    quizzes may be announced or unannounced.
  3. Matrix Calculator Site - Calculates matrix inverse for you.
  4. Matrix Calculator Site - Multiplies matrices for you ( use to check answers )
  5. NCSU Matrix Calculator Site - Will do the "Gauss-Jordon" row reduction for you ("reduce completely" button).
  6. "Wolfram Alpha", I heard a rumor from a reliable source this is something nice to play with.
    I have not since I am a math dinosaur, but if you like technology this may be for you.
  7. Matrix Calculator Site - Will do, well what won't it do? That's the question. Thanks to the student who found this site. Very useful.

III. Test reviews and solutions:
(most of these links are currently not working, I will email you to notify you when something is added here)

IV. Solutions to Homework, Problem Sets and Quizzes:
The solutions will appear as the work is collected.

Weekly Homework Solutions:
  1. Homework 1: on linear systems and Gaussian Elimination
  2. Homework 2: matrix properties, elementary and inverse matrices
  3. Homework 3: calculating inverse matrix, and determinants, Kramer's Rule
  4. Homework 4: spanning sets, linear independence, CCP, coordinate vectors
  5. Homework 5: row, column and null space of a matrix
  6. Homework 6: linear transformations
  7. Homework 7: dot-products, Gram Schmidt, orthogonal complements
  8. Homework 8: orthogonal operators and least square fitting.
  9. Homework 9: inner products, real e-values and e-vectors
  10. Homework 10: e-value theory and complex e-values and vectors
  11. Homework 11: diagonalization and eigenbases
V. Course Notes for Introduction to Linear Algebra:
The text is good, excellent in places. Unfortunately, it does not cover the topics in quite the same order as I envision. Also, there are certain applications that need a more detailed treatment than they're given in the text. Other topics are given more weight than I will give them in my course. I provide these course notes to more closely resemble the core of what is important to this course. These notes, not the text, provide the definitions to be used in this course.

  • Course Notes, just Chapter 1,2,3, 4, and part of 5.

    • Itinerary and week by week reading guide:
    I intend for lecture to cover topics as described below.
    You might find the material is easier to understand if you read ahead.



    VI. Bonus Point Policy:
    It is possible to earn bonus points by asking particularly good questions or suggesting corrections to errors in notes and materials on the course website. This does not include spelling or grammatical errors, those are provided for your amusement. Once I notify the class of the error you may no longer ask for that point.

    These projects are entirely optional. The credit earned is proportional to the quality and quantity of work. Basically I'll just get you started on one of these topics and you get to explain it to me and teach me the topic. These need to be done by the final exam day, do not let them interfere with the regular course work.


    VII. Required Homework List:

    The regular homework tends to be slanted towards the calculational aspects of the course. I have shifted the burden of the harder proof-type problems to the Problem Sets for the most part. I have included a few applications problems in these sets, sometimes I will not cover the application in lecture however the mathematics in lecture will allow you to solve the problem. Fortunately the text is quite readable so I hope you can read it for those problems to learn what you need to set-up the problem. Of course you can ask me where to read if you are unclear on what is being asked. I'm always here to help get you started or un-stuck.

    General Advice: When confronting many "proof" problems in this course (and in more advanced abstract math courses) you ought to ask yourself:
    1. What information is given in the proof?
    2. What is not given? What are we trying to show?
    3. What are the definitions that apply?
    It is not usually the case that you will find the same proof in my notes or the text. Definitions are key, I cannot emphasize this enough. Good hunting.

    Assignment Section # of Spence, Insel and Friedberg Lecture Notes Due Date Problems in the assignment Description / Hints
    Hwk 1 Sec. 1.3 Chapter 1 Aug. 31 4, 46 interpretation of rref
    Hwk 1 Sec. 1.4 Chapter 1 Aug. 31 4, 8, 10, 48 solving systems via Gaussian elimination
    Hwk 1 Sec. 1.5 Chapter 1 Aug. 31 28 application to circuits
    * * * * * * * * * * * * * * * Turn in Hwk 1 at beginning of class on Monday 8-31-09. Solution should be posted on website after class.
    Hwk 2 Sec. 1.2 Chapter 2 Sept. 7 6, 8, 12, 16 matrix multiplication
    Hwk 2 Sec. 2.1 Chapter 2 Sept. 7 10, 12, 14, 16, 50, 71 matrix multiplication and applications
    Hwk 2 Sec. 2.3 Chapter 2 Sept. 7 20, 24, 59 elementary matrices and inverse matrix properties
    * * * * * * * * * * * * * * * Turn in Hwk 2 at beginning of class on Monday 9-7-09. Solution should be posted on website after class.
    Hwk 3 Sec. 2.4 Chapter 2 Sept. 14 8, 60, 67, 84 how to find and use inverse matrices, similar matrix problem
    Hwk 3 Sec. 3.1 Chapter 3 Sept. 14 20, 22, 24, 26, 76 determinants
    Hwk 3 Sec. 3.2 Chapter 3 Sept. 14 8, 66 determinants and Kramer's Rule
    * * * * * * * * * * * * * * * Turn in Hwk 3 at beginning of class on Monday 9-14-09. Solution should be posted on website after class.
    Optional Review . Chapters 1,2,3 Sept. 22 6:50-7:50pm, Science Hall 105. Review For Test I, see Study Guide for Test I for an overview of what is likely on the test I.
    Test I . . Sept. 23 . see study guide for what's on test. Test starts 5 minutes before class, ends 5 minutes after.
    Hwk 4 Sec. 1.6 Chapter 4 Sept. 28 4, 26, 30, 44, 69 spanning sets
    Hwk 4 Sec. 1.7 Chapter 4 Sept. 28 24, 36 linear independence and dependence
    Hwk 4 Sec. 2.3 Chapter 4 Sept. 28 68, 82 column correspondence property
    Hwk 4 Sec. 4.4 Chapter 4 Sept. 28 14, 28 bases and coordinates
    Hwk 4 Sec. 7.1 Chapter 4 Sept. 28 31 spanning in vector space of polynomials
    Hwk 4 Sec. 7.3 Chapter 4 Sept. 28 4 linear independence in vector space of matrices
    * * * * * * * * * * * * * * * Turn in Hwk 4 at beginning of class on Monday 9-28-09. Solution should be posted on website after class.
    Hwk 5 Sec. 1.7 Chapter 4 Oct. 5 54 general solution problem
    Hwk 5 Sec. 4.1 Chapter 4 Oct. 5 20, 28, 82, 90 subspaces; row, column and null space of a matrix.
    Hwk 5 Sec. 4.2 Chapter 4 Oct. 5 6 collumn and null space of a matrix
    Hwk 5 Sec. 4.3 Chapter 4 Oct. 5 4 dimension of subspaces associated with a matrix
    * * * * * * * * * * * * * * * Turn in Hwk 5 at beginning of class on Monday 10-5-09. Solution should be posted on website after class.
    Hwk 6 Sec. 2.7 Chapter 5 Oct. 12 4, 28, 60, 72 linear transformations
    Hwk 6 Sec. 2.8 Chapter 5 Oct. 12 24, 38, 88 matrix of linear transformation, 1-1 property of linear transformation, invertibility of linear transformation
    Hwk 6 Sec. 4.2 Chapter 5 Oct. 12 12 finding a basis for null space and range of linear transformation
    Hwk 6 Sec. 7.2 Chapter 5 Oct. 12 4 linear transformaions on abstract vector spaces
    Hwk 6 Sec. 7.3 Chapter 5 Oct. 12 66 isomorphisms preserve linear independence
    Hwk 6 Sec. 7.4 Chapter 5 Oct. 12 46a-b linear transformaions on abstract vector spaces.
    * * * * * * * * * * * * * * * Turn in Hwk 6 at beginning of class on Monday 10-12-09. Solution should be posted on website after class.
    Optional Review . Chapters 4,5 Oct. 20 6:50-7:50pm, Science Hall 105 Review For Test II, see Study Guide for Test II for an overview of what is likely on the test.
    Test II . . Oct. 21 . see study guide for what's on test. Test starts 5 minutes before class, ends 5 minutes after.
    Hwk 7 6.1 Chapter 6 Oct. 26 4, 14, 38, 52, 87 geometry of vectors in n-dimensions
    Hwk 7 6.2 Chapter 6 Oct. 26 14, 22 orthogonal sets of vectors and dot products
    Hwk 7 6.3 Chapter 6 Oct. 26 2, 6 orthogonal complements
    Hwk 7 6.2 Chapter 6 Oct. 26 63 property of orthogonal matrices
    * * * * * * * * * * * * * * * Turn in Hwk 7 at beginning of class on Monday 10-26-09. Solution should be posted on website after class.
    Hwk 8 6.5 Chapter 6 Nov. 2 39, 42 orthogonal operators and rotations in 3-dimensions
    Hwk 8 6.4 Chapter 6 Nov. 2 2, 16, 38* least squares fitting, closest vector solution, *you may use technology to do #38.
    * * * * * * * * * * * * * * * Turn in Hwk 8 at beginning of class on Monday 11-2-09. Solution should be posted on website after class.
    Hwk 9 7.5 Chapter 6 Nov. 9 6, 12, 20, 47, 72 inner product problems
    Hwk 9 Sec. 5.2 Chapter 7 Nov. 9 14, 16, 38, 34 find eigenvalues and eigenvectors.
    * * * * * * * * * * * * * * * Turn in Hwk 9 at beginning of class on Monday 11-9-09. Solution should be posted on website after class.
    Hwk 10 Sec. 5.1 Chapter 7 Nov. 16 66, 69, 73 simple proofs on eigenvectors/values.
    Hwk 10 Sec. 5.2 Chapter 7 Nov. 16 48 complex eigenvalues/vectors
    * * * * * * * * * * * * * * * Turn in Hwk 10 at beginning of class on Monday 11-16-09. Solution should be posted on website after class.
    Hwk 11 Sec. 5.3 Chapter 7 Nov. 30 14, 22, 82 diagonalization of matrices
    Hwk 11 Sec. 5.4 Chapter 7 Nov. 30 9, 22, 26 eigenvectors of linear operator and eigenbases
    * * * * * * * * * * * * * * * Turn in Hwk 11 at beginning of class on Monday 11-30-09. Solution should be posted on website after class.
    Optional Review . Chapters 6,7 Dec. 1 6:50-7:50pm, Science Hall 105. Review For Test III, see Study Guide for Test III for an overview of what is likely on the test I.
    Test III . . Dec. 2 . see study guide for what's on test. Test starts 5 minutes before class, ends 5 minutes after.
    Hwk 12 n/a Chapter 7 Dec. 7 click here for the homework problems calculus of matrices and solving x' = Ax for constant matrix A. Material not treated in textbook, see my course notes for guidance.
    * * * * * * * * * * * * * * * Turn in Hwk 12 at beginning of class on Monday 12-7-09. Solution should be posted on website after class.
    BONUS 2.6 N/A 12-14-09 17-32 (16 problems) LU-factorization of matrices.
    BONUS 6.2 N/A 12-14-09 25-40 (15 problems) QR-factorization of matrices.
    BONUS 6.6 N/A 12-14-09 2-20(evens), 60, 66 spectral decomposition of matrices, conic sections and rotations,postive definite property.
    BONUS 6.7 N/A 12-14-09 2-10(even), 30-36(even), 38-46(even) singular value decomposition of matrices.
    * * * * * * * * * * * * * * * Turn in BONUS on (or before) 12-14-09 [ notice that you can think of this as a bonus homework, only 500pts are needed for your homework score yet this homework brings the total number of points to more than 500, I think 500+300, certain problems in this set are beyond the lectured material. Time will probably not allow for complete discussions of the various matrix factorization schemes]
    Final Final . at official date at official time comprehensive




    (these links will work once I post the assignments for this semester) Back to my Home

    Last Modified: 10-4-09