Math 201-NYC-05
Vectors and Matrices

ANNOUNCEMENTS:  Test #3 is on Tuesday, November 19.

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

* All documents (videos, transcripts, problem sheets and class notes) can be downloaded directly from any school computer.
   The folder can be found by accessing the public drive. The exact pathway is: P:\Courses\pcamire\Math NYC.
   The total size is about 30 GB.

Tests
Test #1 - Monday, September 16.
Test #2 - Monday, October 21.
Test #3 - Tuesday, November 19.

 


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
Row Reduction & Uniqueness - pdf   7:41
Homogeneous Linear Systems - pdf   7:02 

Gauss-Jordan Elimination - 1
- pdf   14:20
Gauss-Jordan Elimination - 2 - pdf   11:06
Gauss-Jordan Elimination - 3 - pdf   8:31
Gaussian Elimination - Parabolas
- pdf   9:55
Families of Linear Systems - 1
- pdf   15:48
Families of Linear Systems - 2 - pdf   11:06
Families of Linear Systems - 3
- pdf   11:15
Gaussian Elimination - Nonlinear Systems
- pdf   8:02 
3.
 2:17:16
Matrices - Introduction - pdf   23:59
Matrix Operations - Part 1
- pdf   18:04
Matrix Operations - Part 2
- pdf   1:02:21
The Zero Matrix - pdf   7:00
The Identity Matrix - pdf   17:32
Matrices and Polynomials
- pdf   8:20
4.
 45:11
Properties of Matrix Algebra - pdf   45:11
5.
 35:32
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
6.
 1:10:30
Matrix Inverse - Introduction - pdf   12:03
Matrix Inverse - Negative Powers - pdf   4:33
Matrix Multiplication & Linear Systems
- pdf   17:01
Matrix Inverse - Algorithm
- pdf   16:20
Matrix Inverse - Properties
- pdf   13:32
Linear Systems - Number of Solutions - pdf   7:01
7.
 35:12
Elementary Matrices - Part 1 - pdf   12:42
Elementary Matrices - Part 2 - pdf   3:42
Elementary Matrices - Part 3 - pdf   18:48
8.

9-10.
  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
11.
  1:13:09
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
12.
  30:00
Cryptography - Part 1
- pdf   23:25
Cryptography - Part 2
- pdf   6:35
13.
  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

14.
  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
15.
  29:16
Linear Combinations
- pdf   29:16
16.
  3:48:27
Norm and Angles in R^n
- pdf   32:28
Linear Independence
- pdf   30:09
The Span of Vectors
- pdf   46:34
Basis, Dimension, Kernel and Image
- pdf   56:57
Bases and Orthogonality
- pdf   28:26
The Gram-Schmidt Algorithm
- pdf   33:53
17.
  3:54:35
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
Real Vector Spaces - Dimension  - pdf   20:05
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





Old Version

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
Row Reduction & Uniqueness - pdf   7:41
Homogeneous Linear Systems - pdf   7:02 
Gauss-Jordan Elimination - 1 - pdf   14:20
Gauss-Jordan Elimination - 2 - pdf   11:06
Gauss-Jordan Elimination - 3 - pdf   8:31
Gaussian Elimination - Parabolas - pdf   9:55
Families of Linear Systems - 1 - pdf   15:48
Families of Linear Systems - 2 - pdf   11:06
Families of Linear Systems - 3 - pdf   11:15
Gaussian Elimination - Nonlinear Systems - pdf   8:02 
3.  2:17:16
Matrices - Introduction - pdf   23:59
Matrix Operations - Part 1 - pdf   18:04
Matrix Operations - Part 2 - pdf   1:02:21
The Zero Matrix - pdf   7:00
The Identity Matrix - pdf   17:32
Matrices and Polynomials - pdf   8:20
4.  45:11
Properties of Matrix Algebra - pdf   45:11
5.  35:32
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
6.  1:10:30
Matrix Inverse - Introduction - pdf   12:03
Matrix Inverse - Negative Powers - pdf   4:33
Matrix Multiplication & Linear Systems - pdf   17:01
Matrix Inverse - Algorithm - pdf   16:20
Matrix Inverse - Properties - pdf   13:32
Linear Systems - Number of Solutions - pdf   7:01
7.  35:12
Elementary Matrices - Part 1 - pdf   12:42
Elementary Matrices - Part 2 - pdf   3:42
Elementary Matrices - Part 3 - pdf   18:48
8.

9-10.  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
11.  1:13:09
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
12.  30:00
Cryptography - Part 1 - pdf   23:25
Cryptography - Part 2 - pdf   6:35
13.  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
14.  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
15.  29:16
Linear Combinations - pdf   29:16
16.  3:48:27
Norm and Angles in R^n - pdf   32:28
Linear Independence - pdf   30:09
The Span of Vectors - pdf   46:34
Basis, Dimension, Kernel and Image - pdf   56:57
Bases and Orthogonality - pdf   28:26
The Gram-Schmidt Algorithm - pdf   33:53
17.  3:54:35
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
Real Vector Spaces - Dimension  - pdf   20:05
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



 






Problem Sheets

1 - Linear Systems

2 -
Gaussian Elimination
3 - Matrix Operations
4 - Properties of Matrix Algebra
 
5 - Trace & Transpose
6 - Matrix Algebra & Inverses
7 - Elementary Matrices
8 - Additional Problems
9 - Determinants
10 - Determinants - Additional Problems
11 - Eigenvalues
12 - Cryptography (
Optional)
13 - Geometric Vectors
14 - Algebraic Vectors
15 - Linear Combinations
16 -
Euclidean Vector Spaces
17 - Real Vector Spaces
 

Optional Problem Sheets
Balancing Chemical Reactions
Electric Circuits
Matrix Exponential
Markov Chains
Linear Transformations
Inner Product Spaces


Class Notes (Under construction...)
Linear Systems
Linear Systems - Additional Problems
Row Reduction - Two Algorithms
Row Reduction - Examples
Matrices
Matrices & Invertibility  
Axioms of Real Vector Spaces



Additional Documents
Cryptography - Maple Code
Transformation Matrices
Inner Product Spaces
- Maple Code
 The Riemann Zeta Function