 # Systems of Equations and Matrices

Videos and lessons with examples and solutions 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)

### 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

Using a Matrix Equation to Solve a System of Equations
This video shows how to solve a system of equations by using a matrix equation. The graphing calculator is integrated into the lesson.
Ex 1: Solve a System of Two Equations Using a Matrix Equation
This video explains how to solve a system of two linear equations with two unknowns using a matrix equation.

Ex 2: Solve a System of Two Equations Using a Matrix Equation
This video explains how to solve a system of two linear equations with two unknowns using a matrix equation.

Matrices to solve a system of equations
Using the inverse of a matrix to solve a system of equations.

Ex: Solve a System of Three Equations Using a Matrix Equation
This video explains how to solve a system of three linear equations with three unknowns using a matrix equation. Use a calculator to find the inverse of the 3 × 3 matrix.

Solve a 3 variable system with a matrix in the calculator.

## Matrix Calculator

### 3×3 Inverse Matrix Calculator

Enter in your 3×3 matrix to get the inverse.

### 4×4 Matrix Multiplication

Enter in the two 4×4 matrices that you want to multiply

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. 