The 1st column is for coefficient of x1, 2nd column is for coefficient of x2, and so on. The input with C1, C2, etc are for constants

# Cramer's Rule Calculator

Solve the system of Linear equation using Mathcalcs' Cramer's Rule Calculator. Enter the coefficients of the variables and the constants in the input fields and click on the "Calculate" button to get the result.

If you have any concern about the result of the calculator, please let us know using the feedback form below.

## How to use Cramer's Rule Calculator?

To use this cramer's rule calculator, follow the steps below:

- Select the dimension of the square matrix from select box.
- Enter the coefficients of the variables and the constants in the input fields.
- Click on the "Solve" button to get the result.

The first column of the matrix is the coefficients of the variable **x1**, the second column is the coefficients of the variable **x2** and so on

The calculator will give the value of the variables in the system of linear equations.

## What is Cramer's Rule?

Cramer's rule is a mathematical theorem that provides way to solve the system of linear equations using determinants of the matrix formed by the coefficients of the variables and the constants.

The cramer's rule works only for square matrix, which means the number of equations should be equal to the number of variables.

Also the rows or columns of the matrix should be linearly independent.

## Cramer's Rule Formula

The formula to solve the system of linear equations using Cramer's rule is given below:

\(x1 = det(A1) / det(A) -- (1)
\)

\(x2 = det(A2) / det(A) -- (2)
\)

\(x3 = det(A3) / det(A) -- (3)
\)

\(...
xn = det(An) / det(A) -- (n)
\)

Where:

**x1, x2, x3, ..., xn** are the variables in the system of linear equations.**det(A1), det(A2), det(A3), ..., det(An)** are the determinants of the matrix formed by replacing the first, second, third, ..., nth column of the matrix of coefficients with the constants.

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