Related Topics:

More Algebra Lessons

More Lessons on Matrices

Videos, solutions, worksheets, games and activities to help Algebra students learn how to solve 3×3 systems of equations using the inverse of matrices.

We also have a matrix calculator that you can use to calculate the inverse of a 3×3 matrix.

**How to solve a system of three linear equations with three unknowns using a matrix equation?**

Example:

Solve the system using a matrix equation. (Use a calculator)

x + 2y - z = 7

2x - 3y - 4z = -3

x + y + z = 0

**Solving 3-Variable Systems**

Matrix Method

Solving a system of equations with 3 variables.

Example:

4x + 2y - 2z = 10

2x + 8y + 4z = 32

30x + 12y - 4z = 24

**Matrix Equations to solve a 3x3 system of equations**

Example:

Write the matrix equation to represent the system, then use an inverse matrix to solve it. (Use a calculator)

5x - 2y + 4x = 0

2x - 3y + 5z = 8

3x + 4y - 3z = -11

**Solving a 3 × 3 System of Equations Using the Inverse**

Example:

Solve the system of equations using an inverse matrix. (Don't use a calculator)

x + 2y + 2z = 5

3x - 2y + z = 6

2x + y - z = -1

**Solving systems of Equations using Matrices**

Using Inverse Matrices to evaluate a system of equations. (Use a calculator)

Example:

3x - 2y + z = 24

2x + 2y + 2z = 12

x + 5y - 2z = -31

This is a calculator that can help you find the inverse of a 3×3 matrix.

More Algebra Lessons

More Lessons on Matrices

Videos, solutions, worksheets, games and activities to help Algebra students learn how to solve 3×3 systems of equations using the inverse of matrices.

We also have a matrix calculator that you can use to calculate the inverse of a 3×3 matrix.

Example:

Solve the system using a matrix equation. (Use a calculator)

x + 2y - z = 7

2x - 3y - 4z = -3

x + y + z = 0

Matrix Method

Solving a system of equations with 3 variables.

Example:

4x + 2y - 2z = 10

2x + 8y + 4z = 32

30x + 12y - 4z = 24

Example:

Write the matrix equation to represent the system, then use an inverse matrix to solve it. (Use a calculator)

5x - 2y + 4x = 0

2x - 3y + 5z = 8

3x + 4y - 3z = -11

Example:

Solve the system of equations using an inverse matrix. (Don't use a calculator)

x + 2y + 2z = 5

3x - 2y + z = 6

2x + y - z = -1

Using Inverse Matrices to evaluate a system of equations. (Use a calculator)

Example:

3x - 2y + z = 24

2x + 2y + 2z = 12

x + 5y - 2z = -31

This is a calculator that can help you find the inverse of a 3×3 matrix.

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

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.