# Systems of Equations and Augmented Matrices

Related Topics:
Common Core (Algebra)
Common Core for Mathematics

Examples, solutions, 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 x 3 or greater)

### Suggested Learning Targets

• 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

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.

### Row Echelon Form

Augmented Matrices: 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.

### Reduced Row Echelon Form

Augmented Matrices: Reduced Row Echelon Form
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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