# Math 225 Spring 2009 (Intro Matrix Theory)

https://faculty.math.illinois.edu/~jlebl/math225-s09.html

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

Homework

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.

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
```