Videos and lessons to help High School students learn how to
represent a system of linear equations as a single matrix equation
in a vector variable.

Find the inverse of a matrix if it exists and use it to solve
systems of linear equations (using technology for matrices of
dimension 3 × 3 or greater)

- Write a system of linear equations as a single matrix equation.
- Find the inverse of the coefficient matrix in the equation, if it exits. Use the inverse of the coefficient matrix to solve the system. Use technology for matrices with dimensions 3 by 3 or greater.

Common Core: HSA-REI.C.8, HSA-REI.C.9

Related Topics:

Common Core
(Algebra)

Common Core
for Mathematics

Introduction to Augmented Matrices

This video introduces augmented matrices for the purpose of solving systems of equations. It also introduces row echelon and reduced row echelon form.

This video shows how to transform and augmented matrix to row echelon form to solve a system of equations.

Ex 1: Solve a System of Two Equations with Using an Augmented Matrix (Row Echelon Form)

This video provides an example of how to solve a system of two linear equations with two unknowns by writing an augmented matrix in row echelon form. This example has one solution.

Ex 2: Solve a System of Two Equations with Using an Augmented Matrix (Row Echelon Form)

This video provides an example of how to solve a system of two linear equations with two unknowns by writing an augmented matrix in row echelon form. This example has no solution.

Ex 3: Solve a System of Two Equations with Using an Augmented Matrix (Row Echelon Form)

This video provides an example of how to solve a system of two linear equations with two unknowns by writing an augmented matrix in row echelon form. This example has infinite solutions.

This video shows how to transform and augmented matrix to reduced row echelon form to solve a system of equations.

Ex 1: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form)

This video explains how to solve a system of equations by writing an augmented matrix in reduced row echelon form. This example has one solution.

Ex 2: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form)

This video explains how to solve a system of equations by writing an augmented matrix in reduced row echelon form. This example has no solution.

Ex 3: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form)

This video explains how to solve a system of equations by writing an augmented matrix in reduced row echelon form. This example has an infinite number of solutions.

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.