# Solve 3 by 3 System Using Inverse Matrix - Calculators

This calculator solves a 3 by 3 systems of equations using the method of the inverse matrix.

The system of equations is written as

A X = K
where A is a 3 by 3 matrix whose elements are the coefficients of the unknown x, y and z in the system of equations, X is the 3 by 1 matrix whose elements are the unknown x, y and z and K is the 3 by 1 matrix whose elements are the constant terms on the right side of the equations. The solution is given by

X = A^{-1}K
where A^{-1} is the inverse matrix of matrix A.

## Use the Calculator to Solve System

Enter the coefficients in the cells of the 3 by 3 matrix.(decimal, fraction of the form a/b and whole numbers as shown in the example below, are accepted), enter also the constant coefficients of the system on the right side, then press "Solve".
### More References and links

Solve Systems of Equations

The Inverse of a Square Matrix

Cramer's Rule to Solve Systems of Equations

Maths Calculators and Solvers.