Linear equation calculator
Solve the linear system of equations with coefficient and right side. Check for no solution, unique solution, free variable, and row elimination steps.
Input
Calculate directly using the sample value, or try changing the value.
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Result
Check the result using the example value.
Calculation·solution process
Verification of calculation data
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Calculation criteria and usage method
Verify solutions and free variables of a first-order linear equation by elimination of the determinant.
Input example
If x₁+x₂=3, 2 and x₁−x₂=0, then x₁=1, x₂=2. Enter the right-hand side of each equation in the last column.
The first row 1 1 3 is x₁+x₂=3. The second row 2 -1 0 is 2x₁−x₂=0. Since x₂=2x₁ in the second equation, substituting into the first equation gives 3x₁=3, so x₁=1 and x₂=2. If 1 1 3 and 2 2 6 are entered, one variable remains as it is a multiple of the same equation.
How to use
- Use the example value or enter numbers directly. The table format has one row per line.
- Click Verify result. Incorrect rows are marked and excluded.
- Check the result and calculation process, then copy or save the required result as a file.
Limitations and interpretation
Up to 8 equations·8 unknowns. Approximate error calculations. Normalize the coefficient size per row and apply the pivot tolerance. The judgment for almost singular equations may vary depending on the tolerance.
Frequently Asked Questions
What does the result show when there are infinitely many results?
Indicates a year with free variable set to 0 and a vector to add per free variable. All years are sums of arbitrary multiples of the vector for that year.
Can you enter a precise fraction or symbol?
Only number coefficients are supported. Enter the prime and the right side instead of 1/3 or x+y=3. After normalizing rows and determining pivots with tolerance, almost unusual expressions may vary based on settings.
Calculation criteria and reference materials
- MathWorks — finite difference trapezoidal rule
Interpretation of row elimination·pivot and augmented matrix. This tool uses a separate row normalization tolerance.
Verification of calculation criteria: · Calculation·verification principles · Report errors