Introduction to Linear Algebra

The University of Sydney develops linear algebra from geometric vectors in the plane and in space. Lines, planes and systems lead into matrix arithmetic, determinants and eigenvectors, with applications including Markov processes. The geometric emphasis makes it an alternative to a course organized primarily around programming or machine-learning examples.

What you will learn

• Relate vector equations to lines and planes.
• Use elimination and inverses to analyze systems.
• Interpret eigenvectors and simple Markov transformations.

Who this suits

Coursera labels this intermediate. The course recommends studying introductory calculus before or alongside it, and the published workload is substantial.

Before you enroll

The introductory title refers to the subject sequence rather than a short overview. Set aside time for symbolic calculations, readings and assessed problems.

Coursera lists paid enrollment or subscription access. Check the enrollment screen for included assessments, certificate terms, trials and any financial-aid options. University authorship does not by itself confer admission, academic credit or a professional license.

Put it into practice

Describe a line and a plane with vector equations, then solve for their intersection. Draw the geometry and explain when the algebra instead indicates no unique intersection.

Source and review

This overview is based on the provider's published information, checked on 12 October 2026. It is an editorial assessment, not a claim that we completed the resource. Time filters are approximate study ranges; projects and exercises can take longer.

View the curriculum and current access options at Coursera.

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