# Mastering Linear Algebra and Group Theory for 2023

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:

• 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).