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.

**Assessment**

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.

**Certification**

Edukite courses are free to study. To successfully complete a course you must submit all the assignment of the course as part of the assessment. Upon successful completion of a course, you can choose to make your achievement formal by obtaining your Certificate at a cost of £49.

Having an Official Edukite Certification is a great way to celebrate and share your success. You can:

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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 | ||

Assessment | |||

Submit Your Assignment | 00:00:00 | ||

Certification | 00:00:00 |

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