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.