Gaussian elimination is a method to solve systems of linear equations by simplifying a matrix using row operations. If that sounds complicated, don’t worry!
A Gaussian elimination calculator is an online tool that performs these calculations for you. If you are struggling to solve these problems yourself, this tool can help you.
Understanding Gaussian Elimination
Gaussian elimination is a way to solve a system of linear equations by simplifying a matrix (a rectangular array of numbers or other mathematical objects) into what’s known as row echelon form. You may also know it as Gauss-Jordan elimination, which is essentially the same process.
During the process, you’ll perform row operations (subtracting, multiplying, or dividing) to simplify the matrix. Augmented matrices are used to represent the equations, and when complete, the matrix will be in row echelon form or reduced row echelon form (RREF).
How to use a Gaussian elimination calculator
Entering equations and matrices
Most Gaussian elimination calculators let you enter integers, decimals, or fractions.
It’s important to arrange your equations so the variables line up in columns. If a variable is missing from one of the equations, enter “0” as its coefficient.
Some calculators also let you change the variable names if you want.
How to read the results
A good Gaussian elimination calculator will give you the answer one step at a time, so you can see exactly how the solution was reached.
Many calculators also offer a “complete reduction” option if you want to see the final answer right away.
In Conclusion
A Gaussian elimination calculator simplifies complex calculations and is a useful tool for anyone solving linear equations, especially students and educators learning about linear algebra.