Linear Algebra: Linear Systems and Matrix Equations

Joseph Cutrone begins the Johns Hopkins sequence with two questions: whether a linear system has a solution, and whether that solution is unique. Row reduction, vectors and matrix equations provide the tools to answer them. The course then connects those computations with linear transformations, emphasizing definitions and reasoning as well as procedural accuracy.

What you will learn

• Use pivots to analyze a system’s solutions.
• Express linear combinations as matrix equations.
• Recognize when a function is a linear transformation.

Who this suits

The provider does not require previous linear algebra or calculus. Comfort rearranging ordinary equations is still useful for the worked examples.

Before you enroll

This is the opening course in a sequence. Its final assessment checks foundational concepts; determinants and deeper eigenvector theory belong to later study.

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

Construct one system with a unique solution and another with infinitely many solutions. Row-reduce both, then explain the different pivot patterns in plain language.

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.

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