# Gaussian elimination calculator

# Gaussian elimination calculator

Gaussian elimination, also known as row reduction, is a method for solving linear systems of equations. It works by manipulating a matrix that represents the system of equations through a sequence of row operations until it is transformed into an equivalent matrix that is in row echelon form or reduced row echelon form. Here’s how to use a calculator for Gaussian elimination:

- Enter the coefficients of the variables and the constants in the linear system of equations in the form of an augmented matrix.
- Apply row operations on the matrix until it is in row echelon form. The row operations are:
- Interchange two rows
- Multiply a row by a nonzero constant
- Add a multiple of one row to another row

- Apply back substitution to the row echelon matrix to get the solution(s) to the system of equations.

Note that some calculators may have a built-in Gaussian elimination function or program. If your calculator has this function, simply follow the prompts to enter the matrix and obtain the solution(s).

### Gaussian elimination step by step

Gaussian elimination is a method used to solve a system of linear equations by reducing the augmented matrix to row echelon form through a series of row operations. Here are the steps involved:

- Write the augmented matrix of the system of linear equations.
- Begin with the first column of the matrix and look for a nonzero element in the column starting from the top row.
- If there is no nonzero element in the first row, swap it with a row below it that has a nonzero element in the first column.
- Divide the first row by the first nonzero element to make it equal to 1.
- Use row operations to make all the elements below the first element in the first column equal to 0.
- Move to the next column and repeat steps 2-5 until the matrix is in row echelon form.
- Back substitute to obtain the solutions to the system of linear equations.

Note that row operations include adding a multiple of one row to another, multiplying a row by a nonzero constant, or interchanging two rows.