**Section N1:** TR 10:00-10:50 pm in 145
Altgeld

**Lecturer:** Jiří Lebl

Web: https://faculty.math.illinois.edu/~jlebl/

Office: 105 Altgeld

E-mail:
jle...@math.uiuc.edu

Phone: 3-3143

Office hours: MW 1:00pm-1:50pm, W 3:00 - 3:50pm, and by appointment

**Grades/Curve: ** Grades will be based on the percentages below. Curve
will be applied if needed.

**Midterm 1: ** Thursday, February 26, 25% of your grade.

**Midterm 2: ** Thursday, April 16, 25% of your grade.

**Final Exam: ** 1:30 - 4:30 PM, Wednesday, May 13, 40% of your grade.

**Homework:** Assigned every week. Worth
10%, possibly spot checked (*spot checked* means: some spot(s) of each
homework checked, and all will be collected). Lowest homework grade dropped.

**Test Policies:** No books, notes, calculators or computers allowed on
the exams or the final.

** Text: **
David C. Lay, *Linear Algebra and its Applications*, 3rd Edition, Addison-Wesley, 2002.

**Syllabus:** (Approximately one section per lecture)

# Chapter 1: Linear Equations in Linear Algebra * 1.1 Systems of Linear Equations * 1.2 Row Reduction and Echelon Forms * 1.3 Vector Equations * 1.4 The Matrix Equation Ax=b * 1.5 Solution Sets of Linear Systems * 1.6 Applications * 1.7 Linear Independence # Chapter 2: * 2.1 Matrix Operations * 2.2 The Inverse of a Matrix * 2.3 Characterizations of Invertible Matrices * 2.6 The Leontief Input-Output Model # Chapter 3: Determinants * 3.1 Introduction to Determinants * 3.2 Properties of Determinants * 3.3 Cramer's Rule, Volume, and Linear Transformations # Chapter 4: Vector Spaces * 4.1 Vector Spaces and Subspaces * 4.2 Null spaces, Column Spaces, and Linear Transformations * 4.3 Linearly Independent Sets: Bases * 4.5 The Dimension of a Vector Space * 4.6 Rank # Chapter 5: Eigenvalues and Eigenvectors * 5.1 Eigenvalues and Eigenvectors * 5.2 The Characteristic Equation * 5.3 Diagonalization # Chapter 6: Orthogonality and Least Squares * 6.1 Inner Product, Length, and Orthogonality * 6.2 Orthogonal Sets * 6.3 Orthogonal Projections * 6.5 Least Squares Problems * 6.6 Applications to Linear Models