Enter coefficients for a 4x4 linear system. Review elimination results, determinant status, and plotted outputs. Export tables and keep solved values for reference easily.
Fill the coefficients for x, y, z, and w. Then enter the constants on the right side.
| Equation | x | y | z | w | Constant |
|---|---|---|---|---|---|
| 1 | 2 | 1 | -1 | 3 | 10 |
| 2 | 1 | -2 | 4 | 1 | 5 |
| 3 | 3 | 0 | 1 | -2 | 4 |
| 4 | 1 | 5 | -1 | 2 | 12 |
Use the example loader to populate these values automatically.
The calculator solves a four-equation linear system written as A × X = B.
Here, A is the 4×4 coefficient matrix, X is the variable vector, and B is the constants vector.
The main method is Gaussian elimination with partial pivoting. It transforms the augmented matrix into reduced row echelon form. That reveals whether the system has one solution, no solution, or infinitely many solutions.
For a unique solution, the determinant of the coefficient matrix is nonzero. Then the system is nonsingular, and each variable can be read directly from the final reduced matrix.
It solves four simultaneous linear equations with four unknowns. It also reports determinant value, matrix ranks, reduced row echelon form, and the final system classification.
A zero determinant means the coefficient matrix is singular. The system may then have no solution or infinitely many solutions, depending on the ranks of the coefficient and augmented matrices.
Ranks help classify the system. If both ranks match and equal four, the solution is unique. If ranks differ, the system is inconsistent. If equal but below four, infinitely many solutions exist.
It is a simplified matrix form created by row operations. In that form, pivot positions are clear, and solution values can be read directly for uniquely solvable systems.
Yes. The inputs accept integers and decimals. The solver uses floating-point arithmetic, so it can handle common practical systems with non-integer values.
The graph displays solved values of x, y, z, and w as bars. It helps compare magnitudes quickly after a unique solution is found.
They show the row operations used to reach the final matrix. This helps with learning, checking work, and understanding how the solution was obtained.
Export when you need a saved record, want to share the solved values, or need documentation for homework, reports, or technical analysis.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.