Dave4Math / Courses / Linear Systems and Matrices

Linear Systems and Matrices

Master linear systems and matrices. Learn Gaussian elimination, operations with matrices, inverse matrices, and determinants. In this course, you'll become skilled at using Gaussian elimination to solve linear systems.


January 11, 2021

Created by Dave

This course begins Summer 2021.
Current Status
Not Enrolled
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How else should a teacher’s effectiveness be judged other than helpfulness? Helpful in teaching students how to ask great questions, teach them how to experiment, plan, be interesting, be concise, and share their curiosity. Introducing Dave’s online math course: Linear Systems and Matrices. In this course, Dave is your biggest cheerleader.

Who This Course is For

  • Students in college who want to learn more mathematics.
  • Anyone interested in linear systems and matrices.
  • Students who are enrolled in precalculus and want to improve their grade.
  • Anyone interested in getting prepared for calculus 1.
  • Anyone wanting to learn about solving linear systems of equations, matrices, operations with matrices, and the inverse of a matrix.


There is no required textbook, though you will need an up-to-date web browser, paper, and pen. A hand-held scientific calculator of your choice is required.

What You’ll Learn in Linear Systems and Matrices

  • Substitution Method
  • Graphing Method
  • Points of Intersection
  • The Method of Elimination
  • Applications
  • Interpretation of  2-Variable Systems
  • Row-Echelon Form
  • Back-Substitution
  • Gaussian Elimination
  • Nonsquare Systems
  • Matrices
  • Elementary Row Operations
  • Equality of Matrices
  • Matrix Multiplication
  • Interpretation of 3-Variable Systems
  • Back-Substitution
  • Matrix Addition
  • Scalar Multiplication
  • The Inverse of a Matrix
  • Finding Inverse Matrices
  • The Inverse of a 2 by 2 Matrix
  • Systems of Linear Equations
  • The Determinant of a 2 by 2 Matrix
  • Minors and Cofactors
  • The Determinant of a Square Matrix
  • Triangular Matrices
  • Area of a Triangle
  • Collinear Points
  • Cramer’s Rule
  • Cryptography

Course Description

I recommend the prerequisite course Linear Systems and Matrices. If you’re not sure if this course is for you, checkout the course contents below or find out more by checking out my free precalculus articles.

Course Content

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David A. Smith

Mathematics Educator

I sincerely believe that the potential in every student can be unlocked. As an accomplished and dedicated instructor, I have firm confidence that I can provide significant value to your studies.

I relish teaching and use it as a channel for my creativity as I seek to deliver real-life and relevant connections between the mathematics that I teach and my students. Promoting an active learning environment and excitement about mathematics is my dream come true.

David Smith (Dave) has a B.S. and M.S. in Mathematics and has enjoyed teaching precalculus, calculus, linear algebra, and number theory at both the junior college and university levels for over 20 years. David is the founder and CEO of Dave4Math.