Math 3
Chapter 1: Linear Algebra
1
1. Systems of Linear Equations
1.1 Introduction to Systems of Linear Equations1.2 Elimination method for solving systems of linear equations1.4 Methods for Solving Linear Systems of Equations
Vectors | Chapter 1, Essence of linear algebra
3Blue1Brown
1.1
Lecture 1: The Geometry of Linear Equations
Gilbert Strang (MIT)
1.1
The Gaussian Algorithm Visualized
Dr. Trefor Bazett
1.21.4
Row Echelon Form and Reduced Row Echelon Form
Dr. Trefor Bazett
1.21.4
2
2. Matrices and Matrix Operations
1.3 Matrices and Matrix Operations1.5 Inverse of a Matrix Using Gauss-Jordan reduction
Linear combinations, span, and basis vectors
3Blue1Brown
1.3
Matrix multiplication as composition
3Blue1Brown
1.3
Lecture 2: Elimination with Matrices
Gilbert Strang (MIT)
1.3
Lecture 3: Multiplication and Inverse Matrices
Gilbert Strang (MIT)
1.31.5
3
3. The Matrix Eigen-Value Problem
2.1 Geometric interpretation2.2 Eigenvalues2.3 Properties of Eigenvalues and Eigenvectors2.4 Cayley-Hamilton (C. H.) Theorem and its Applications2.5 Diagonalization of Matrices
Eigenvectors and eigenvalues
3Blue1Brown
2.12.2
Lecture 21: Eigenvalues and Eigenvectors
Gilbert Strang (MIT)
2.22.3
Lecture 22: Diagonalization and Powers of A
Gilbert Strang (MIT)
2.5
The Cayley-Hamilton theorem
Dr. Trefor Bazett
2.4
4
4. Determinants
3.1 Definition3.2 Properties of Determinants3.3 Determinants by Cofactor Expansion
The determinant
3Blue1Brown
3.13.2
How to Find the Determinant of a 3x3 Matrix
The Organic Chemistry Tutor
3.1
The Determinant of a 4 by 4 Matrix Using Cofactor Expansion (Expansion by Minors)
Mathispower4u
3.3