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DelftX: Linear Algebra I: Vectors and Linear Equations

This course provides an overview of bachelor-level linear algebra. You will review all the concepts and practice and refresh the skills related to vectors and linear equations.

Linear Algebra I: Vectors and Linear Equations
6 weeks
4–6 hours per week
Self-paced
Progress at your own speed
Free
Optional upgrade available

There is one session available:

After a course session ends, it will be archivedOpens in a new tab.
Starts Dec 3

About this course

Skip About this course

A strong foundation in mathematics is critical for success in all science and engineering disciplines. Whether you want to make a strong start to a master’s degree, prepare for more advanced courses, solidify your knowledge in a professional context or simply brush up on fundamentals, this course will get you up to speed.

In many engineering master’s programs, you need to be familiar with linear algebra. This course will enable you to review the relevant topics.

This course focuses on vectors (from both algebraic and geometric perspectives) and solving linear equations. It will help you refresh your knowledge, test your skills and review the relations between the many concepts in linear algebra.

The linear algebra courses within this series will offer you an overview of this branch of mathematics common to most engineering bachelor’s programs. They provide enough depth to cover the linear algebra you need to succeed in your engineering master’s or profession in areas such as computer graphics, systems and control, machine learning, quantum computing and more.

This is a review course
This self-contained course is modular, so you do not need to follow the entire course if you wish to focus on a particular aspect. As a review course you are expected to have previously studied or be familiar with most of the material. Hence the pace will be higher than in an introductory course.

This format is ideal for refreshing your bachelor level mathematics and letting you practice as much as you want. Through the Grasple platform, you will have access to plenty of exercises and receive intelligent, personal and immediate feedback.

This course is part of our series Mastering Mathematics for Engineers , and together with the course Linear Algebra II part of the program Mastering Linear Algebra.

At a glance

  • Institution: DelftX
  • Subject: Math
  • Level: Intermediate
  • Prerequisites:

    Prior knowledge of all the material covered.

    This is a self-contained bachelor-level course. However, we do assume that you are familiar with standard high school mathematics, specifically standard functions and their properties, algebraic manipulation of equations and inequalities and standard mathematical notation.

    This course is a review course. As such the course requires you to have studied linear algebra in the past or are at least familiar with its course contents. If this is not the case for you, then you can still do the course, but be prepared for a high pace!

  • Language: English
  • Video Transcripts: اَلْعَرَبِيَّةُ, Deutsch, English, Español, Français, हिन्दी, Bahasa Indonesia, Português, Kiswahili, తెలుగు, Türkçe, 中文
  • Associated programs:
  • Associated skills:Basic Math, Linear Algebra, Linear Equations, Machine Learning, Quantum Computing

What you'll learn

Skip What you'll learn
  • Apply the dot product and cross product.
  • Describe lines, planes and their intersections.
  • Solve systems of linear equations and describe the solution set.
  • Decide whether vectors are linear dependent or not.
  • Recognize linear subspaces, describe elements of linear subspaces using bases and coordinates.
  • Calculate projections and orthogonal decompositions of vectors.
  • Find least-square solutions of a system of linear equations and apply it to regression.

Week 1: Vectors

  • calculating with vectors
  • the dot product
  • the cross product
  • lines and planes

Week 2: Linear equations

  • systems of equations
  • solving systems of equations
  • structure of the solutions set

Week 3: Linear dependence

  • linear combinations
  • linear dependence
  • relations between concepts

Week 4: Linear subspaces

  • What are linear subspaces?
  • basis and coordinates
  • dimension
  • the rank theorem

Week 5: Orthogonality

  • orthogonal sets
  • orthogonal projections
  • the Gram-Schmidt algorithm
  • orthogonal complements
  • transposition

Week 6: Least square solutions

  • "solving” an inconsistent system
  • normal equations
  • application to regression

Frequently Asked Questions

Skip Frequently Asked Questions

Q: I am going to start a master’s in engineering. Is this MOOC mandatory?
A: It is not mandatory, but we believe it could be useful to revisit some of these topics.

Q: Can I use the certificate I get from this MOOC to get an exemption from a certain course?
A: No, you cannot. That is not the goal of these courses.

Q: Can I use this MOOC as a substitute for the Bridging Programme (Schakelprogramma)?
A: No, you cannot.

Q: What level is required to follow this course?
A: It is a review course. Hence the pace will be a bit higher than when you learn about these topics for the first time. However, every concept within linear algebra will be explained.

Q: What is the duration of this course?
A: You will probably need 4 to 6 hours per week, for 6 weeks.

Q: I am going to follow this MOOC. Will I have to hand in homework?
A: No. The exercises will be checked automatically, and you will get immediate feedback.

This course is part of Mastering Linear Algebra Professional Certificate Program

Learn more 
Expert instruction
2 skill-building courses
Self-paced
Progress at your own speed
3 months
4 - 6 hours per week

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