Solve system of equations reduced row echelon form calculator

Here you can solve systems of simultaneous linear equations using Gauss-Jordan Elimination Calculator with complex numbers online for free with a very detailed solution. Our calculator is capable of solving systems with a single unique solution as well as undetermined systems which have infinitely many solutions. In that case you will get the dependence of one variables on the others that are called free. You can also check your linear system of equations on consistency using our Gauss-Jordan Elimination Calculator.

Have questions? Read the instructions.

About the method

To solve a system of linear equations using Gauss-Jordan elimination you need to do the following steps.

1. Set an augmented matrix.
2. In fact Gauss-Jordan elimination algorithm is divided into forward elimination and back substitution. Forward elimination of Gauss-Jordan calculator reduces matrix to row echelon form. Back substitution of Gauss-Jordan calculator reduces matrix to reduced row echelon form. But practically it is more convenient to eliminate all elements below and above at once when using Gauss-Jordan elimination calculator. Our calculator uses this method.
3. It is important to notice that while calculating using Gauss-Jordan calculator if a matrix has at least one zero row with NONzero right hand side (column of constant terms) the system of equations is inconsistent then. The solution set of such system of linear equations doesn't exist.

To understand Gauss-Jordan elimination algorithm better input any example, choose "very detailed solution" option and examine the solution.