Linear Algebra
part 1 of 3

A total of 46 hours of lectures

This is an academic level course for university and college engineering. Due to its size, it is divided into three parts. This page describes the first of those three parts.

Prerequisites

High-school maths, mainly arithmetics, some trigonometry

Curriculum

Make sure that you check with your professor what parts of the course you will need for your exam. Such things vary from country to country, from university to university, and they can even vary from year to year at the same university.

Linear Algebra, part 1 of 3

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Get the outline

A detailed list of all the lectures in part 1 of the course, including which theorems will be discussed and which problems will be solved. If you are looking for a particular kind of problem or a particular concept, this is where you should look first.

Get Linear Algebra part 1 on Udemy

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Course Objectives & Outcomes for part 1

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How to solve problems in linear algebra and geometry (illustrated with 175 solved problems) and why these methods work.
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Interpret geometrically solution sets of systems of linear equations by analysing their RREF matrix (row equivalent with the augmented matrix of the system).
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Matrix inverse: determine whether a matrix is invertible; compute its inverse: both with (Jacobi) algorithm and by the explicit formula; matrix equations.
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Vectors, their coordinates and norm; geometrical vectors and abstract vectors, their addition and scaling: arithmetically and geometrically (in 2D and 3D).
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Analytical geometry in the 3-space: different ways of describing lines and planes, with applications in problem solving.
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Determine whether lines and planes are parallel, and compute the angles between them (using dot product and directional or normal vectors) if they intersect.
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Understand the connection between systems of linear equations and matrix multiplication.
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Solve systems of linear equations with help of Gauss-Jordan or Gaussian elimination, the latter followed by back-substitution.
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Matrix operations (addition, scaling, multiplication), how they are defined, how they are applied, and what computational rules hold for them.
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Determinants, their definition, properties, and different ways of computing them; determinant equations; Cramer’s rule for n-by-n systems of equations.
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Vector products (scaling, dot product, cross product, scalar triple product), their properties and applications; orthogonal projection and vector decomposition.
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Compute distances between points, planes and lines in the 3-space, both by using orthogonal projections and by geometrical reasoning.
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How to geometrically interpret n-by-2 and n-by-3 systems of equations and their solution sets as intersection sets between lines in 2D or planes in 3D.
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Invertible Matrix Theorem and its applications; apply determinant test in various situations
Teenapong S.
Udemy student
I know many things in this course which I never knew before. The instructor dives into the detail with clearly explanation.
Gabi O.
Udemy student
Great linear algebra course ever!
Edward P.
Udemy student
I haven't finished even 1 percent of this course but I'm compelled to give a 5 star rating because the teacher has made a good impression on me in the first video. She explained the cordinates systems in a unique way that I will never forget. Thanks for being a beautiful teacher.
Artem B.
Udemy student
The course is awesome! First I solve a problem, then I watch how the professor solves it. And after having completed the course, I must say that it is greatly structured: the chapters are self-sufficient, but by the end of the course you feel pretty distinctly how every piece of it fits into the overall picture. The last chapters on analytic geometry are the most rewarding in that regard, where you can operate employing all the learned concepts.

The only drawback for me is that the lectures are a bit too verbose, often explaining elementary things. But I have a degree in Applied Math and the most of the concepts are known to me. So it might as well be that what is a drawback for me would become a blessing for you.

Hope that helps you to decide.

And I'd like to thank prof. Uscka-Wehlou for the great course!
Щиро дякую вам, професорко! Точно візьму ваш наступний курс, адже прийшов сюди заради власних векторів (eigenvectors) та власних значень (eigenvalues).
Farzad R.
Udemy student
Outstanding perspicuity as always
Jim W.
Udemy student
very well done
Hock T.
Udemy student
very detailed. Exaclty what I need. Thanks, Hania.
James S.
Udemy student
My first class, and I'm really enthusiastic about the quality of instruction. Very good pace and thorough.
Tan N.
Udemy student
I watched the introduction and the beginning video (coordinate systems) and found the explanations clear and concise, the pace is suitable for me as well, hopefully I will be much better at maths by the end of this course! 🙂
Daniel S.
Udemy student
This is a splendid course in an absolutely foundational topic, with detailed explanations and examples, and presented at a gentle pace that anyone with thorough preparation in high school mathematics can easily maintain.