Linear Algebra: Free Course

About this course

Study vectors, matrices and transformations in this free Linear Algebra course from Khan Academy. The complete 144-video collection develops the language of vector spaces, systems, linear maps, subspaces, coordinate choices and projections. Its explanations connect operations with geometric and structural meaning, helping a prepared learner understand what a calculation represents and when a relationship can be used.

Course at a glance

What you’ll learn

• Work with vectors, matrices and systems of linear equations.
• Explore span, independence, subspaces and the structure of a vector space.
• Interpret a matrix as a transformation and analyze its properties.
• Study projections, bases and alternate coordinate systems.
• Connect calculations with definitions and check the conditions supporting a result.

Skills you’ll gain

• Linear algebra
• Vector spaces
• Matrix transformations
• Subspaces
• Coordinate systems
• Projections

Course Overview

The complete recorded edition covers the three main teaching areas represented in the source: vectors and spaces, matrix transformations and alternate coordinate systems. It includes foundational matrix recordings, structural explanations, demonstrations and later geometric examples. Rather than treating a matrix operation as an isolated rule, the learner can connect it with the map, space or system it describes. All 144 source entries remain available, including supporting recordings that are also found in other mathematics courses. A strong study approach combines a manageable calculation with an explanation of the definitions and conditions behind it.

How to study the course

• Videos 1–36: this part of the source list includes “Introduction to matrices” through “Null space 3: Relation to linear independence”. Write definitions and assumptions explicitly. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 37–72: this part of the source list includes “Column space of a matrix” through “Exploring the solution set of Ax = b”. Track the mathematical objects used in each operation. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 73–108: this part of the source list includes “Matrix condition for one-to-one trans” through “Showing that A-transpose x A is invertible”. Compare a simple example with a less obvious one. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 109–144: this part of the source list includes “Projections onto subspaces” through “Distance between planes”. Verify the solution using its defining conditions. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits prepared college-level learners and returning students studying the specific advanced topic. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

The earlier algebra or calculus used in the recordings is assumed. Keep working notes and review definitions before following a proof or a multistep calculation.

Put the lessons into practice

Choose a small set of vectors and examine the relationships taught in the recordings. Organize an appropriate calculation as a matrix problem, identify the relevant space or transformation and explain the result. Change one vector or coefficient and compare the cases. For a coordinate or projection example, state the basis or subspace involved and check that the answer satisfies its defining relationship. Keep a diagram or simple numerical case beside the symbolic work. Finish by explaining one result in terms of the structure it represents rather than only listing the operations performed.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.