Mastering Linear Algebra and Group Theory for 2023

Learn Linear Algebra Concepts with simple examples.
Free tutorial
Rating: 4.8 out of 5 (23 ratings)
1,688 students
1hr 1min of on-demand video
English [Auto]

You will analyze the solution set of a system of linear equations.
Learn elemantary matrix operations.
Express a system of linear equations in a matrix form.
Perform the elementary row operations for the matrices and systems of linear equations.
Learn Gauss Elimination.
Solve systems of linear equations using the inverse of the coefficient matrix when possible


  • Simple math basics


  • 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

Who this course is for:

  • Academic Students.
  • School Students.


Azure Data Engineer and Instructor
Atchyut Kumar
  • 4.4 Instructor Rating
  • 1,325 Reviews
  • 24,240 Students
  • 15 Courses

Atchyut Kumar is  a renowned programming and GATE CS/IT expert!

With a Masters from the prestigious National Institute of Technology-Calicut and a remarkable GATE CS/IT top ranker with an exceptional 99.97 percentile, Atchyut brings a wealth of knowledge and expertise to our Azure Data Engineering training.

Having spent 6+ years in database development and as a skilled Data Engineer, Atchyut possesses a remarkable 7+ years of experience as a GATE faculty. In total, he boasts an impressive 13+ years of teaching, research, and industry experience, having successfully mentored over 50,000 students through both classroom and online courses.

Atchyut is not only an expert in problem-solving techniques, algorithms, and competitive programming, but he also holds a specialization in data integration, transformation, and consolidation from various structured, unstructured, and streaming data systems. This unique skill set enables him to construct suitable schemas for building robust analytics solutions.

His unparalleled guidance has paved the way for many of his former students, who are now thriving in esteemed organizations such as Amazon, Samsung, Oracle, Google, Adobe, and many others. Some have even pursued higher studies, such as MS, M Tech, or Ph.D., further emphasizing the quality and impact of his teaching.

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