• Course Description

This is a first undergraduate course in linear algebra. The course starts with concrete topics such as systems of linear equations, and matrices with which a typical student should already have some familiarity at elementary level. Abstract concepts such as a vector space, a linear transformation acting on the vector spaces are first introduced in connection with these concrete grounds. Second part introduces topics such as vector spaces, isomorphism, transformations in abstract terms and in a general setting. The course concludes with eigenvalue problems, and the notions of an inner product and orthogonality.

• Announcements

February 12, Friday: Have a good semester.

February 12, Friday: There will be no problem sessions during the first week (the week of Feb 15-19). Problem sessions will start in the second week, and will be held every week from there on

February 12, Friday: Most of the announcements, if not all, will be made through blackboard or by e-mails sent by your instructor.

March 20, Saturday: The first midterm will be held on March 21st Sunday between 9:30 – 11:30 through blackboard. The topics covered by this midterm are those related to Sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.7, 1.8 1.9, 2.1, 2.2 from the textbook. Please read the instructions to take Midterm 1 before the exam.

• Syllabus

Click on here for the syllabus

• Calendar

1. Week 1 (Feb 15 – 19)
   Systems of Linear Equations, Row Reduction and Echelon Forms (1.1-1.2)
2. Week 2 (Feb 22 – 26)
   Vector Equations, Matrix Equation Ax = b, Solution Sets of Linear Systems (1.3-1.5)
3. Week 3 (Mar 1 – 5)
   Linear Independence in Rn, Introduction to Linear Transformations (1.7-1.8)
4. Week 4 (Mar 8 – 12)
   Matrix of a Linear Transformation, Matrix Operations (1.9, 2.1)
5. Week 5 (Mar 15 – 19)
   Inverse of a Matrix, Characterizations of Invertible Matrices, Vector Spaces and Subspaces (2.2-2.3, 4.1)
6. Week 6 (Mar 22 – 26)
   Null Spaces, Column Spaces, Linear Transformations on Vector Spaces, Linear Independence, Basis (4.2-4.3)
7. Week 7 (Mar 29 – Apr 3)
   Coordinate Systems, Isomorphism, Dimension of a Vector Space (4.4-4.5)
8. Week 8 (Apr 12 – 16)
   Rank, Change of Bases (4.6-4.7)
9. Week 9 (Apr 19 – 23)
   Introduction to Determinants, Properties of Determinants, Cramer’s Rule (3.1-3.3)
10. Week 10 (Apr 26 – 30)
    Eigenvalues and Eigenvectors, Characteristic Equation (5.1-5.2)
11. Week 11 (May 3 – 7)
    Diagonalization, Eigenvectors and Linear Transformations, Complex Eigenvalues (5.3-5.5)
12. Week 12 (May 10 – 14)
    Inner Product, Length, Orthogonality, Orthogonal Sets (6.1-2)
13. Week 13 (May 17 – 21)
    Orthogonal Projections, Gram-Schmidt Process, Least-Squares Problem (6.3-6.5)
14. Week 14 (May 24 – 28)
    Inner Product Spaces, Symmetric Eigenvalue Problem (6.7, 7.1)
15. Finals (May 31 – June 11)

• Homework

Homework questions are posted here, but your solutions will not be collected. Sections refer to the textbook by Lay, Lay and McDonald.

1. Week 1 Questions (Sections 1.1-1.3)
2. Week 2 Questions (Sections 1.3-1.4)
3. Week 3 Questions (Sections 1.5, 1.7-1.9)
4. Week 4 Questions (Sections 1.9, 2.1-2.2)
5. Week 5 Questions (Sections 2.2-2.3)
6. Week 6 Questions (Sections 4.1-4.3) – Solutions to Selected Week 6 Questions
7. Week 7 Questions (Sections 4.2-4.4) – Solutions to Selected Week 7 Questions
8. Week 8 Questions (Sections 4.4-4.6)
9. Week 9 Questions (Section 4.7)
10. Week 10 Questions (Sections 3.1-3.3 and 5.1-5.2) – Solutions to Selected Week 10 Questions
11. Week 11 Questions (Sections 5.2-5.4)
12. Week 12 Questions (Sections 5.4-5.5)
13. Week 13 Questions (Sections 6.1-6.5, 6.7) – Solutions to Selected Week 13 Questions

• Exam

Exam from Spring 2020:

1. Midterm 1 – Solutions
2. Midterm 2 – Part 1 – Solutions
3. Midterm 2 – Part 2 – Solutions
4. Final – Solutions

Exam from Spring 2017:

1. Midterm 1 – Solutions
2. Midterm 2 – Solutions
3. Midterm 3 – Solutions
4. Final – Solutions

Current Semester