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Solving 3×3 Systems of Equations using Matrices

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
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



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



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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.


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