Mastering Linear Algebra and Group Theory for 2023, Learn Linear Algebra Concepts with simple examples.

## Course Description

- analyze the solution set of a system of linear equations.
- express some algebraic concepts (such as binary operation, group, field).
- do elementary matrix operations.
- express a system of linear equations in a matrix form.
- do the elementary row operations for the matrices and systems of linear equations.
- investigate the solution of a system using Gauss elimination.
- apply Cramer’s rule for solving a system of linear equations, if the determinant of the matrix of coefficients of the system is not zero.
- generalize the concepts of a real (complex) vector space to an arbitrary finite-dimensional vector space.
- definite a vector space and subspace of a vector space.
- explain properties of R^n and sub-spaces of R^n.
- determine whether a subset of a vector space is linear dependent.
- describe the concept of a basis for a vector space.
- investigate properties of vector spaces and sub-spaces using by linear transformations.
- express linear transformation between vector spaces.
- represent linear transformations by matrices.
- explain what happens to representing matrices when the ordered basis is changed.
- describe the concepts of eigenvalue, eigenvector and characteristic polynomial.
- determine whether a linear transformation is diagonalizable or not.

**Who this course is for:**

- Academic Students.
- Competitive Exam Preparation Aspirants.

**Important information before you enroll!**

- Once enrolled, you have unlimited, 24/7,
**lifetime access**to the course (unless you choose to drop the course during the first 30 days). - You will have
**instant and free access**to any updates I’ll add to the course – video lectures, additional resources, quizzes, exercises. - You will benefit from my full support regarding any question you might have.
- Check out the promo video at the top of this page and some of the free preview lectures in the curriculum to get a taste of my teaching style and methods before making your decision