MATH 3110 · Linear Algebra

Lecture Notes

Shuhong Gao  ·  Clemson University

These notes are interactive. Click any dotted term to unfold its exact definition or statement right where you are reading — no scrolling back. Click ▸ Proof to expand a proof, and answer the self-check exercises inline: they are graded instantly in your browser, and nothing is recorded.

Lectures

  1. Lecture 1: Vectors, Matrices, and Systems of Linear Equations

    Vector arithmetic, the product Ax read by rows and by columns, linear systems, elementary operations, and the matrix equation Ax = b.

  2. Lecture 2: Gaussian Elimination and Solution Sets

    Echelon forms, the elimination algorithm, free variables, the parametric vector form, and the existence–uniqueness theorem.

  3. Lecture 3: Homogeneous Systems, Independence, and Linear Maps

    Homogeneous systems and the structure of solution sets, linear independence, linear maps, and the correspondence between matrices and linear maps.

How to use these notes

Each lecture is one week's material. Read the intuition paragraphs first — every section opens with the idea before the formalism. The self-check exercises inside the notes are for practice only; the graded problem set for each week is posted separately on Canvas.