Gauss-Jordan elimination calculator
Here you can solve a system of simultaneous linear equations online using Gauss-Jordan elimination calculator for free with a very detailed solution. Moreover this calculator is capable of solving systems online 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 others that are called free. You can also check your linear equation system on consistency online using 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.
- Set an augmented matrix.
- 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.
- 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 online better take any example, choose "very detailed solution" option and examine the solution online.