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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

**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.

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.

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)

- 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.

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.

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.

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.

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.

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.

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.

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.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

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.

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