Math 201-105-RE
Linear Algebra

ANNOUNCEMENTS: 

Term Schedule
Office Hours
Math Workshop Schedule
Offline Web Page
Academic Calendar
Course Outline
Math Department Web Page

Tests
Test #1 - Thursday, February 6.
Test #2 - Wednesday, March 11.
Test #3 -

 



MyYoutube
1-2.
 4:04:36
Linear Equations
- pdf   18:03
Systems of Linear Equations - pdf   11:34
Linear Systems & Geometry
- pdf   15:25
Augmented Matrix
- pdf   11:51
Elementary Row Operations
- pdf   26:43
Row Reduction Algorithm
- pdf   16:05
Gaussian Elimination - 1
- pdf   6:30
Gaussian Elimination - 2
- pdf   9:54
Gaussian Elimination - 3
- pdf   8:39
Gaussian Elimination - 4 - pdf   15:06
Gaussian Elimination - Parabolas -
pdf   9:55
Gaussian Elimination - Nonlinear Systems -
pdf   8:02 
Gauss-Jordan Elimination - 1
- pdf   14:20
Gauss-Jordan Elimination - 2 - pdf   11:06
Gauss-Jordan Elimination - 3 - pdf   8:31
Row Reduction & Uniqueness - pdf   7:41
Homogeneous Linear Systems - pdf   7:02
Families of Linear Systems - 1
- pdf   15:48
Families of Linear Systems - 2 - pdf   11:06
Families of Linear Systems - 3
- pdf   11:15 
3.
  1:56:14
Matrices - Introduction
- pdf   23:59
Matrix Operations - Part 1
- pdf   18:04 - Optional
Matrix Operations - Part 2
- pdf   1:02:21 - Optional
Matrix Operations (Part 1 & 2 Condensed) - pdf   30:28
Matrix Operations - Part 3 - pdf   (Skip to 23 minutes.)   22:11
The Zero Matrix
- pdf   7:00
The Identity Matrix - pdf   17:32
Matrix Multiplication & Linear Systems - pdf   9:15 
Powers of Matrices - pdf   5:49
4.
 30:41
The Trace of a Square Matrix -
pdf   14:04
The Transpose of a Matrix -
pdf   16:37
A Property of the Transpose -
pdf   4:51 - Optional
5.
  1:14:43
Matrices and Polynomials -
pdf   8:20 
Linear Systems - Number of Solutions - pdf   7:01
Matrix Inverse - Introduction
- pdf   12:03
Matrix Inverse - Algorithm -
pdf   16:20
Matrix Inverse & Linear Systems - pdf   12:55
Matrix Inverse - Properties
- pdf   13:32
Matrix Inverse - Negative Powers - pdf   4:33
6.
 35:12
Elementary Matrices - Part 1 - pdf   12:42
Elementary Matrices - Part 2 - pdf   3:42
Elementary Matrices - Part 3 - pdf   18:48
7.

8-9.
  2:22:22
The Determinant - Part 1 - pdf   26:13
The Determinant - Part 2 - pdf   19:37
The Determinant - Part 3 - pdf   19:40
The Determinant - Part 4 - pdf   18:21
The Determinant - Additional Problems - pdf   27:38
The Adjoint Formula - Part 1
- pdf   9:34
The Adjoint Formula - Part 2
- pdf   9:04
Cramer's Rule - pdf   12:15

10.
  1:13:09 - Optional
Eigenvalues - Introduction
- pdf   21:37
Eigenvalues - Application 1
- pdf   16:56
Eigenvalues - Application 2
- pdf   21:46
A Proof that P^-1AP=D
- pdf   12:50
11.

12.
  30:00
Cryptography - Part 1
- pdf   23:25
Cryptography - Part 2
- pdf   6:35
13.

14.
  1:17:00
Geometric Vectors - Theory
- pdf   21:18
Geometric Vectors - Problem 1
- pdf   6:46
Geometric Vectors - Problem 2
- pdf   11:14
Geometric Vectors - Problem 3
- pdf   11:10
Geometric Vectors - Problem 4
- pdf   9:04
Geometric Vectors - Problem 5
- pdf   17:28
15.
  4:26:20
Algebraic Vectors - Introduction
- pdf   16:21
Algebraic Norm
- pdf   13:21
The Dot Product - Part 1
- pdf   18:23
The Dot Product - Part 2
- pdf   17:04
Orthogonal Projections - Part 1
- pdf   21:38
Orthogonal Projections - Part 2
- pdf   28:28
The Cross Product - Part 1
- pdf   25:25
The Cross Product - Part 2
- pdf   33:04
Lines in R^3
- pdf   34:17
Planes in R^3
- pdf   26:32
Intersections - Lines and Planes
- pdf   31:47
16.
  29:16
Linear Combinations
- pdf   29:16
17.
  3:48:27
Norm and Angles in R^n
- pdf   32:28
Linear Independence
- pdf   30:09
The Span of Vectors
- pdf   46:34  (23:16-38:35 is optional.)
Basis, Dimension, Kernel and Image
- pdf   56:57
Bases and Orthogonality
- pdf   28:26
The Gram-Schmidt Algorithm
- pdf   33:53
18.
  3:12:56
Real Vector Spaces - Introduction
- pdf   20:31
Subspace Theorem - Introduction - pdf   30:07
Subspace Theorem - Examples - pdf   17:03
Functions as Vectors - Intuition - pdf   12:59
Linear Independence - #1 - pdf   23:24
Linear Independence - #2
- pdf   21:34  - Optional
Real Vector Spaces - Dimension  - pdf   20:05 - Optional
Dimension & Linear Dependence
- pdf   23:12
Subspace Theorem & Basis - #1
- pdf   23:54
Subspace Theorem & Basis - #2
- pdf   14:58
Subspace Theorem & Basis - #3 - pdf   26:48

19.  1:21:25
Linear Optimization - Introduction - pdf   12:40
Geometric Solution - 1 - pdf   12:25
Simplex Method - 1 - pdf   16:35
Simplex Method - 2 - pdf   15:15
Simplex Method - 3 - pdf   24:30




Old Version


MyYouTube

1-2.
Linear Equations
Systems of Linear Equations
Linear Systems & Geometry
Augmented Matrix
Elementary Row Operations
Row Reduction Algorithm
Gaussian Elimination - 1
Gaussian Elimination - 2
Gaussian Elimination - 3
Gaussian Elimination - 4
Gaussian Elimination - Parabolas
Gaussian Elimination - Nonlinear Systems
Gauss-Jordan Elimination - 1
Gauss-Jordan Elimination - 2
Gauss-Jordan Elimination - 3
Row Reduction & Uniqueness
Homogeneous Linear Systems
Families of Linear Systems - 1
Families of Linear Systems - 2
Families of Linear Systems - 3
3-4.
Matrices - Introduction
Matrix Operations - Part 1 (Optional)
Matrix Operations - Part 2 (Optional)
Matrix Operations (Part 1 & 2 Condensed)
Matrix Operations - Part 3 (Skip to 23 min.)
The Zero Matrix
The Identity Matrix
Matrix Multiplication & Linear Systems
A Proof that AI=A (Optional)
Powers of Matrices
The Trace of a Square Matrix
The Transpose of a Matrix
A Property of the Transpose (Optional)
5-6-7.
Matrices and Polynomials
Linear Systems - Number of Solutions
Matrix Inverse - Introduction
Matrix Inverse - Algorithm
Matrix Inverse & Linear Systems
Matrix Inverse - Properties
Matrix Inverse - Negative Powers
Elementary Matrices - Part 1
Elementary Matrices - Part 2
Elementary Matrices - Part 3
8-9.
The Determinant - Part 1
The Determinant - Part 2
The Determinant - Part 3
The Determinant - Part 4
The Determinant - Additional Problems
The Adjoint Formula - Part 1
The Adjoint Formula - Part 2
Cramer's Rule
10. (Optional)
Eigenvalues - Introduction
Eigenvalues - Application 1
Eigenvalues - Application 2
12.
Cryptography - Part 1
Cryptography - Part 2
14.
Geometric Vectors - Theory
Geometric Vectors - Problem 1
Geometric Vectors - Problem 2
Geometric Vectors - Problem 3
Geometric Vectors - Problem 4
Geometric Vectors - Problem 5
15.
Algebraic Vectors - Introduction
Algebraic Norm
The Dot Product - Part 1
The Dot Product - Part 2
Orthogonal Projections - Part 1
Orthogonal Projections - Part 2
The Cross Product - Part 1
The Cross Product - Part 2
Lines in R^3
Planes in R^3
Intersections - Lines and Planes
16-17.
Norm and Angles in R^n
Linear Combinations
Linear Independence
The Span of Vectors (23:16-38:35 is optional)
Basis, Dimension, Kernel and Image
Bases and Orthogonality
The Gram-Schmidt Algorithm
18.
Real Vector Spaces - Introduction
Subspace Theorem - Introduction
Subspace Theorem - Examples
Functions as Vectors - Intuition
Linear Independence - #1
Linear Independence - #2 (Optional)

Real Vector Spaces - Dimension (Optional)
Dimension & Linear Dependence
Subspace Theorem & Basis - #1
Subspace Theorem & Basis - #2
Subspace Theorem & Basis - #3
19.
Linear Optimization - Introduction
Geometric Solution - 1
Simplex Method - 1
Simplex Method - 2
Simplex Method - 3





Documents
Row Reduction - Two Algorithms
Row Reduction - Examples
Transformation Matrices
(Optional)
Cryptography (Maple code - Optional)
Axioms of Real Vector Spaces
The Simplex Method

Problem Sheets

 1 -
Linear Systems
 2 - Gaussian Elimination
 3 - Matrix Operations  
 4 - Trace & Transpose 
 5 - Matrix Algebra & Inverses
 6 - Elementary Matrices 
 7 - Additional Problems 
 8 - Determinants  
 9 - Determinants - Additional Problems
 10 - Eigenvalues
  (Optional)
 11 - Markov Chains  (Optional)
 12 - Cryptography 
 
13 - Linear Transformations  (Optional)
 14 - Geometric Vectors  
 15 - Algebraic Vectors  
 
 16 - Linear Combinations 
 17 - Euclidean Vector Spaces  
 18 - Real Vector Spaces 
 19 - The Simplex Method


Notes (
Under construction...)
Linear Systems
Linear Systems - Additional Problems
Matrices
Matrices & Invertibility