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Become a Linear Algebra Master (Udemy.com)

Learn everything from Linear Algebra, then test your knowledge with 400+ practice questions

Created by: Krista King

Last updated June 2026

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What you will learn

  • Operations on one matrix, including solving linear systems, and Gauss-Jordan elimination
  • Operations on two matrices, including matrix multiplication and elimination matrices
  • Matrices as vectors, including linear combinations and span, linear independence, and subspaces
  • Dot products and cross products, including the Cauchy-Schwarz and vector triangle inequalities
  • Matrix-vector products, including the null and column spaces, and solving Ax=b
  • Transformations, including linear transformations, projections, and composition of transformations
  • Inverses, including invertible and singular matrices, and solving systems with inverse matrices
  • Determinants, including upper and lower triangular matrices, and Cramer's rule
  • Transposes, including their determinants, and the null (left null) and column (row) spaces of the transpose

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Course Description

HOW BECOME A LINEAR ALGEBRA MASTER IS SET UP TO MAKE COMPLICATED MATH EASY:

This 247-lesson course includes video and text explanations of everything from Linear Algebra, and it includes 69 quizzes (with solutions!) and an additional 12 workbooks with extra practice problems, to help you test your understanding along the way. Become a Linear Algebra Master is organized into the following sections:

  • Operations on one matrix, including solving linear systems, and Gauss-Jordan elimination

  • Operations on two matrices, including matrix multiplication and elimination matrices

  • Matrices as vectors, including linear combinations and span, linear independence, and subspaces

  • Dot products and cross products, including the Cauchy-Schwarz and vector triangle inequalities

  • Matrix-vector products, including the null and column spaces, and solving Ax=b

  • Transformations, including linear transformations, projections, and composition of transformations

  • Inverses, including invertible and singular matrices, and solving systems with inverse matrices

  • Determinants, including upper and lower triangular matrices, and Cramer's rule

  • Transposes, including their determinants, and the null (left null) and column (row) spaces of the transpose

  • Orthogonality and change of basis, including orthogonal complements, projections onto a subspace, least squares, and changing the basis

  • Orthonormal bases and Gram-Schmidt, including definition of the orthonormal basis, and converting to an orthonormal basis with the Gram-Schmidt process

  • Eigenvalues and Eigenvectors, including finding eigenvalues and their associate eigenvectors and eigenspaces, and eigen in three dimensions



AND HERE'S WHAT YOU GET INSIDE OF EVERY SECTION:

Videos: Watch over my shoulder as I solve problems for every single math issue you’ll encounter in class. We start from the beginning... I explain the problem setup and why I set it up that way, the steps I take and why I take them, how to work through the yucky, fuzzy middle parts, and how to simplify the answer when you get it.

Notes: The notes section of each lesson is where you find the most important things to remember. It’s like Cliff Notes for books, but for math. Everything you need to know to pass your class and nothing you don’t.

Quizzes: When you think you’ve got a good grasp on a topic within a course, you can test your knowledge by taking one of the quizzes. If you pass, great! If not, you can review the videos and notes again or ask for help in the Q&A section.

Workbooks: Want even more practice? When you've finished the section, you can review everything you've learned by working through the bonus workbook. The workbooks include tons of extra practice problems, so they're a great way to solidify what you just learned in that section.



HERE'S WHAT SOME STUDENTS OF BECOME A LINEAR ALGEBRA MASTER HAVE TOLD ME:

  • “Another fantastic course. Provides an academic foundation of linear algebra to prepare for applied or programming-based courses.” - Christopher C.

  • “I have no words to thank Krista for this amazing course, I was really overwhelmed because I had to take a test for a class I couldn't attend and I didn't know anything about linear algebra and surprisingly this course was what I needed, reading the notes before watching the video helped to understand by myself and when I was lost the video content was a great resource, I got a 9 out of 10 in the test, so I highly recommend to take this course, Krista is such a good teacher.” - Alan M.

  • “I started out as a math major in college, and dropped my major during linear algebra. I wish I had this class and this instructor in college. I might have stuck with my major.” - Eric L.

  • “Notes are great, explanations are clear and starting from the beginning. Terrific so far.” - Phil T.

  • “Very clear and has not skipped any steps. If the rest of the course is like this, I will pass my class with no problem.” - Brandon P.

  • “Really well structured and well explained, and there are plenty of exercises to reinforce the knowledge.” - Ashfaque C.



YOU'LL ALSO GET:

  • Lifetime access to Become a Linear Algebra Master

  • Friendly support in the Q&A section

  • Udemy Certificate of Completion available for download

  • 30-day money back guarantee


Enroll today!

I can't wait for you to get started on mastering Linear Algebra.

- Krista :)

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Instructor Details

Krista King

Hey, I’m so glad you’re here! My goal is to help you feel confident and capable in math. In my courses you’ll find clear, step-by-step videos, notes, and tons of practice materials designed to help you learn exactly what you need — so you can save time, truly understand the concepts, and see just how much math you can master.

I teach every level, from Pre-Algebra, Algebra, and Geometry through Trigonometry, Precalculus, and Probability & Statistics, all the way up to Calculus, Differential Equations, and Linear Algebra.

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Reviews

4.8

7,992 ratings on Udemy

Select a bar to show only those reviews.Select the bar again to show every rating.

By Grace Allen on 8/6/2026

I have taken a couple of Miss King's courses, and they have been so much better than the high school and college courses I've taken. Very good instructor that makes math approachable. Would definitely recommend these courses.

By Amar Dewri on 6/21/2026

Among all the courses I have tried to better understand Linear Algebra, this has been by far the most effective. What sets this course apart is its teaching approach. Instead of relying heavily on slides that simply show the starting point and the final answer, the instructor works through the problems step by step and explains the reasoning behind each step. Seeing equations solved in real time, along with clear explanations of the thought process, makes the concepts much easier to understand and retain. For someone who is learning or revisiting mathematics after a long gap, this approach is incredibly valuable. The course focuses not just on the answer, but on how to arrive at the answer, which builds genuine understanding and confidence. Thank you for creating such a practical and well-explained course.

By Brian Wiley on 6/4/2026

I hate ratings. The text for four stars is actually correct because it is about what i expected, but I expected a really good course. And it was. I only have a concern and that is that I learned a lot and appreciate that, but through the course there are these little suggestions that there might be more . . . . like comments similar to "you'd want to be able to change your basis to an orthonormal basis to make things (in a future problem) easier." I believe I understand what was taught (I'll probably go throught the course again to gain a 'second nature" understanding of what I leanred) but I have to imagine a time where I would decide to change to an orthonormal basis before continuing on with a problem. Of course, this is just an example of a niggling feeling I have, that there might be something out there that i might want to do that would require a better understanding of linear algebra. But it seems, unlike calculus, there isn't a "linear algebra II."

By David J Fondale on 5/24/2026

The course presents topics in a straight-forward, understandable manner. I was able to get through it in about a month.. Before the end of the course, I had the breakthrough I needed to finish a project on which I've been working but needed more knowledge of the numbers to complete it. I always kicked myself for not going back to take Linear Algebra in college. Now it's done! Thank you, Krista!

By John Dubchak on 5/23/2026

Krista's explanations, pace, and quality are perfect. This is, by far, the best start to any course I have ever taken and I have taken a lot in my many years of being a student. I look forward to continuing my learning with Krista. Thank you.

By Ami Weil on 4/6/2026

This course is great for understanding the intuition and how to actually solve LA questions. The math is not rigorous, i.e. there are no proofs or lemmas. It covers LA part 1. So it won't cover university level math, but it is a GREAT preparation, because it explains how to solve questions, and why.

By Varda Amir-Orrel on 3/4/2026

I finished all the videos, but warning for anyone else who thinks that they can calculate the time it would take them to finish this course. I had to watch most of the videos at a speed of *0.5 or *0.75 to be able to understand the material. I would have appreciated more visuals that explain the idea of subspace and span. And more real life examples of how one might use each concept. I did like the organization of the sections, as it made much better sense than an actual college class. What could have made this course even better is one lecture at the end that does a recap of all lectures to put it more into perspective of main topics. Also, it would have helped to have one download of all the main formulas and major statements to remember. It could also help to have one video per section that shows a more complex type of question and not the basic one. The type of question that asks "when will this happen?" or "if you are given this, what can you tell me?" or "if this is true, then which one of these statements is false?"

By Chhuon Thao on 2/1/2026

Krista Kink, expained math from a stundent perspective, and you can learn it. She broke down complex concepts into easy to follow and easy to understand process. I finished the class with confident that I have mastered the material. Simply putting, Krista Kink is one of te best math instructor.

By Alexander Verner on 1/18/2026

The course covers a wide range of topics, most of which are covered in depth. The theoretical explanations in the notes are clear and concise, with fully reviewed examples. The lectures may not cover all the details, but are easy to understand. Some advanced chapters are missing, and some claims in the course are mistaken/inaccurate. But the staff is constantly working on fixing them. A very good course in general.

By McDonald Ibekwe on 12/18/2025

It is an amazing course. She did a good job explaining all the concepts. Also, she accompanied it with lots assignment, quizzes, and even an exam. Overall, I recommend this course for anyone trying to learn the foundation of Linear Algebra.

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Overall Score : 96 / 100