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Linear Algebra is one of the branches of mathematics you will encounter in school. Developing your knowledge in this will give you an advantage in applying it to real-life situations especially in disciplines of physics, economics, and natural sciences.

The main objective of this [course_title] is to help you understand both matrix theory and linear algebra. You can utilize what you learned from this to improve your logical skills.


This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.


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Course Credit: MIT

Course Curriculum

The Geometry of Linear Equations 00:39:00
Geometry of Linear Algebra 00:17:00
An Overview of Key Ideas 00:49:00
An Overview of Key Ideas 00:08:00
Elimination with Matrices 00:47:00
Elimination with Matrices 00:10:00
Multiplication and Inverse Matrices 00:46:00
Inverse Matrices 00:08:00
Factorization into A = LU 00:48:00
LU Decomposition 00:10:00
Transposes, Permutations, Vector Spaces 00:47:00
Subspaces of Three Dimensional Space 00:15:00
Column Space and Nullspace 00:46:00
Vector Subspaces 00:09:00
Solving Ax = 0: Pivot Variables, Special Solutions 00:43:00
Solving Ax=0 00:10:00
Solving Ax = b: Row Reduced Form R 00:47:00
Solving Ax=b 00:09:00
Independence, Basis and Dimension 00:50:00
Basis and Dimension 00:08:00
Computing the Four Fundamental Subspaces 00:11:00
Computing the Four Fundamental Subspaces 00:11:00
Matrix Spaces; Rank 1; Small World Graphs 00:45:00
Matrix Spaces 00:09:00
Graphs, Networks, Incidence Matrices 00:47:00
Graphs and Networks 00:12:00
Orthogonal Vectors and Subspaces 00:49:00
Orthogonal Vectors and Subspaces 00:10:00
Projections onto Subspaces 00:48:00
Projection onto Subspaces 00:10:00
Projection Matrices and Least Squares 00:48:00
Least Squares Approximation 00:08:00
Orthogonal Matrices and Gram-Schmidt 00:49:00
Gram-Schmidt Orthogonalization 00:10:00
Properties of Determinants 00:49:00
Properties of Determinants 00:10:00
Determinant Formulas and Cofactors 00:53:00
Determinants 00:13:00
Cramer’s Rule, Inverse Matrix and Volume 00:51:00
Determinants and Volume 00:14:00
Eigenvalues and Eigenvectors 00:51:00
Eigenvalues and Eigenvectors 00:09:00
Diagonalization and Powers of A 00:51:00
Powers of a Matrix 00:09:00
Differential Equations and exp(At) 00:51:00
Differential Equations and exp(At) 00:19:00
Markov Matrices 00:12:00
Symmetric Matrices and Positive Definiteness 00:43:00
Symmetric Matrices and Positive Definiteness 00:13:00
Complex Matrices; Fast Fourier Transform (FFT) 00:47:00
Complex Matrices 00:13:00
Positive Definite Matrices and Minima 00:50:00
Positive Definite Matrices and Minima 00:13:00
Similar Matrices and Jordan Form 00:45:00
Similar Matrices 00:08:00
Singular Value Decomposition 00:41:00
Computing the Singular Value Decomposition 00:12:00
Linear Transformations and their Matrices 00:49:00
Linear Transformations 00:11:00
Change of Basis; Image Compression 00:50:00
Change of Basis 00:12:00
Left and Right Inverses; Pseudoinverse 00:41:00
Pseudoinverses 00:15:00
Submit Your Assignment 00:00:00
Certification 00:00:00

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