Module 1 start

Here are the materials for Module 1.

Textbook sections: 1.1, 1.2

Instructor's Videos:

Lecture 1

Lecture 2

Lecture 3

Prof. Gilbert Strang's Lectures at MIT:

Lecture 1

Lecture 2

Short Videos from Prof. Byerly at TTU:

Solutions of Linear systems

Gaussian Elimination

Echelon Form and Back Substitution

Gauss-Jordan and RREF

REF matrices

A further example of RREF

Calculators and Uniqness of RREF

Module 2

Textbook sections: 2.1-2.4

Instructor's Lecture Videos:

Prof. Byerly's Videos:

Matrix Arithmetic Part 1

Matrix Arithmetic Part 2

Systems as Matrix Equations

Introduction to the Matrix Inverse

Matrix Inverse, First Example

Matrix Inverse, Another Example

Elementary Matrices

Prof. Strang's Lectures

Lecture 2, Elimination with Matrices

Lecture 3, Multiplication and Inverse Matrices

Module 3

Determinants, properties of determinants, cofactors, computing determinants by elimination, inverting matrices using determinants, Cramer's Rule

Textbook Sections: 3.1--3.4

Prof. Byerly's Videos:

Introduction to Determinants

Minors and Cofactors

Examples

Row Operations and Determinants

Examples with Row Operations

The Elimination Method for Determinants

Properties of Determinants

Examples for Properties of Determinants

Adjoints and Inverses

Cramer's Rule

You can follow the Kahn Academy Videos, starting here:

Determinant of a 2 x 2 matrix

Module 4 Materials

Module 4: Vector space, subspaces, spans, linear independence, basis and dimension, spaces associated with a matrix.

Textbook Sessions: 4.1--4.6

(Section 4.7 will be covered in the next module)

Instructor Videos:

Professor Byerly's Videos (with the section in the book)

4.1: Vector Spaces and R^n

4.1: Linear Combinations

4.2: Vector Spaces

4.2: Vector Space Example

4.3: Subspaces

4.3: More on Subspaces

4.3: Examples on Subspaces

4.4: Linear Independence

4.4: Linear Independence Examples

4.4: Linear Independence of Polynomials

4.5: Bases of a Vector Space

4.5: Basis Examples 4.5: Properties of Bases and Dimensions

4.6: Intro to Row and Column Spaces

4.6: Row Space

4.6: Intro to Column Spaces

4.6: Column Space Examples

4.6: More Column Space Examples

4.6: The Null Space

4.6: The Rank plus Nullity Theorem

Prof. Strang's Lectures

Kahn Academy Videos

Start here, follow through to the basis of a subspace

Module 5

Coordinates, Change of Basis, Linear Transformations, Matrices for Linear Transformations,
Change of Basis for Linear Transformation Matrices.

The notes and the instructor videos are the main sources and explain the notation we'll be using.

Lance Drager's Pages

Study Modules

Spring 2020

Math 2360, Linear Algebra

Module 1 start

Module 2

Module 4 Materials

Module 5

Module 6